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<a href="_qp_mc_linear_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="comment">//===========================================================================</span><span class="comment"></span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="comment">/*!</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="comment"> *</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span><span class="comment"> *</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="comment"> * \brief       Quadratic programming solvers for linear multi-class SVM training without bias.</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span><span class="comment"> *</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><span class="comment"> *</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span><span class="comment"> *</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span><span class="comment"> * \author      T. Glasmachers</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span><span class="comment"> * \date        -</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span><span class="comment"> *</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span><span class="comment"> *</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="comment"> * \par Copyright 1995-2017 Shark Development Team</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="comment"> *</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="comment"> * &lt;BR&gt;&lt;HR&gt;</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="comment"> * This file is part of Shark.</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="comment"> * &lt;https://shark-ml.github.io/Shark/&gt;</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="comment"> *</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="comment"> * Shark is free software: you can redistribute it and/or modify</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span><span class="comment"> * it under the terms of the GNU Lesser General Public License as published</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span><span class="comment"> * by the Free Software Foundation, either version 3 of the License, or</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="comment"> * (at your option) any later version.</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span><span class="comment"> *</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span><span class="comment"> * Shark is distributed in the hope that it will be useful,</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span><span class="comment"> * but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span><span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span><span class="comment"> * GNU Lesser General Public License for more details.</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span><span class="comment"> *</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span><span class="comment"> * You should have received a copy of the GNU Lesser General Public License</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span><span class="comment"> * along with Shark.  If not, see &lt;http://www.gnu.org/licenses/&gt;.</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span><span class="comment"> *</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span><span class="comment"> */</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span><span class="comment">//===========================================================================</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span> </div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span> </div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span><span class="preprocessor">#ifndef SHARK_ALGORITHMS_QP_QPMCLINEAR_H</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span><span class="preprocessor">#define SHARK_ALGORITHMS_QP_QPMCLINEAR_H</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span> </div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span><span class="preprocessor">#include &lt;<a class="code" href="_timer_8h.html">shark/Core/Timer.h</a>&gt;</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span><span class="preprocessor">#include &lt;<a class="code" href="_quadratic_program_8h.html">shark/Algorithms/QP/QuadraticProgram.h</a>&gt;</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span><span class="preprocessor">#include &lt;<a class="code" href="_dataset_8h.html">shark/Data/Dataset.h</a>&gt;</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span><span class="preprocessor">#include &lt;<a class="code" href="_data_view_8h.html">shark/Data/DataView.h</a>&gt;</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span><span class="preprocessor">#include &lt;<a class="code" href="_base_8h.html">shark/LinAlg/Base.h</a>&gt;</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span><span class="preprocessor">#include &lt;cmath&gt;</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span><span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span><span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span> </div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span> </div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceshark.html" title="AbstractMultiObjectiveOptimizer.">shark</a> {</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span> </div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span><span class="comment"></span> </div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span><span class="comment">/// \brief Generic solver skeleton for linear multi-class SVM problems.</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span><span class="comment"></span><span class="keyword">template</span> &lt;<span class="keyword">class</span> InputT&gt;</div>
<div class="foldopen" id="foldopen00054" data-start="{" data-end="};">
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear.html">   54</a></span><span class="keyword">class </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>{</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span><span class="keyword">public</span>:</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear.html#a09a8a598fe1e6c6c625be0c55b03985a">   57</a></span>    <span class="keyword">typedef</span> <a class="code hl_class" href="classshark_1_1_labeled_data.html" title="Data set for supervised learning.">LabeledData&lt;InputT, unsigned int&gt;</a> <a class="code hl_typedef" href="classshark_1_1_qp_mc_linear.html#a09a8a598fe1e6c6c625be0c55b03985a">DatasetType</a>;</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear.html#a8da0d0f5ee8a849b350304e391ae0ea1">   58</a></span>    <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code hl_typedef" href="group__shark__globals.html#ga04ea4c6c5368461a8bafa49001695b7d">LabeledData&lt;InputT, unsigned int&gt;::const_element_reference</a> <a class="code hl_typedef" href="classshark_1_1_qp_mc_linear.html#a8da0d0f5ee8a849b350304e391ae0ea1">ElementType</a>;</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear.html#a88e09c2e6decd1e35f0755f0faf982f7">   59</a></span>    <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code hl_struct" href="structshark_1_1_batch.html" title="class which helps using different batch types">Batch&lt;InputT&gt;::const_reference</a> <a class="code hl_typedef" href="classshark_1_1_qp_mc_linear.html#a88e09c2e6decd1e35f0755f0faf982f7">InputReferenceType</a>;</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span> </div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear.html#a844cac01d9113019e1f89de7d0810d79a306e16139b81caaa99ea79d3ede9a712">   61</a></span>    <span class="keyword">enum</span> <a class="code hl_enumeration" href="classshark_1_1_qp_mc_linear.html#a844cac01d9113019e1f89de7d0810d79">CoordinateSelectionStrategy</a> {<a class="code hl_enumvalue" href="classshark_1_1_qp_mc_linear.html#a844cac01d9113019e1f89de7d0810d79ac281d0b5f356d094aa5ad039e28cdc35">UNIFORM</a>, <a class="code hl_enumvalue" href="classshark_1_1_qp_mc_linear.html#a844cac01d9113019e1f89de7d0810d79a306e16139b81caaa99ea79d3ede9a712">ACF</a>};</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span> </div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span><span class="comment"></span> </div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span><span class="comment">    /// \brief Constructor</span></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span><span class="comment">    /// \param  dataset   training data</span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span><span class="comment">    /// \param  dim       problem dimension</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span><span class="comment">    /// \param  classes   number of classes in the problem</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span><span class="comment">    /// \param  strategy  coordinate selection strategy</span></div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span><span class="comment">    /// \param  shrinking flag turning shrinking on and off</span></div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span><span class="comment">    ///</span></div>
<div class="foldopen" id="foldopen00073" data-start="{" data-end="}">
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear.html#a257f16d453818fb33a9b32d8dd7c6bf2">   73</a></span><span class="comment"></span>    <a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#a257f16d453818fb33a9b32d8dd7c6bf2" title="Constructor.">QpMcLinear</a>(</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>            <span class="keyword">const</span> <a class="code hl_class" href="classshark_1_1_labeled_data.html" title="Data set for supervised learning.">DatasetType</a>&amp; dataset,</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>            std::size_t dim,</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>            std::size_t classes,</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>            std::size_t strategy = <a class="code hl_enumvalue" href="classshark_1_1_qp_mc_linear.html#a844cac01d9113019e1f89de7d0810d79a306e16139b81caaa99ea79d3ede9a712">ACF</a>,</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>            <span class="keywordtype">bool</span> shrinking = <span class="keyword">false</span>)</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    : <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">m_data</a>(dataset)</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    , <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#adb2a6e9f3681450a55dd5764648d0cb6" title="diagonal entries of the quadratic matrix">m_xSquared</a>(dataset.numberOfElements())</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    , <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a04cb0e529976e34569d0b6863e36b881" title="input space dimension">m_dim</a>(dim)</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    , <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>(classes)</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    , <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab5489cad6b7a0db6065331414ae21dc7" title="strategy for coordinate selection">m_strategy</a>(strategy)</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    , <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a4881e1ffbdb28a0f2d0fee00373e4e09" title="apply shrinking or not?">m_shrinking</a>(shrinking)</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>    {</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>        <a class="code hl_define" href="_exception_8h.html#a73abb5049a0168d72a48e72dda41708b">SHARK_ASSERT</a>(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a04cb0e529976e34569d0b6863e36b881" title="input space dimension">m_dim</a> &gt; 0);</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span> </div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>        <span class="keywordflow">for</span> (std::size_t i=0; i&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">m_data</a>.size(); i++)</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>        {</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>            <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#adb2a6e9f3681450a55dd5764648d0cb6" title="diagonal entries of the quadratic matrix">m_xSquared</a>(i) = inner_prod(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">m_data</a>[i].input, <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">m_data</a>[i].input);</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>        }</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>    }</div>
</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span><span class="comment"></span> </div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span><span class="comment">    /// \brief Solve the SVM training problem.</span></div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span><span class="comment">    /// \param  rng      random number generator used by the algorithm</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span><span class="comment">    /// \param  C        regularization constant of the SVM</span></div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span><span class="comment">    /// \param  stop     stopping condition(s)</span></div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span><span class="comment">    /// \param  prop     solution properties</span></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span><span class="comment">    /// \param  verbose  if true, the solver prints status information and solution statistics</span></div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span><span class="comment">    ///</span></div>
<div class="foldopen" id="foldopen00103" data-start="{" data-end="}">
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear.html#a468f877984aab4f95122083bf4a87152">  103</a></span><span class="comment"></span>    RealMatrix <a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#a468f877984aab4f95122083bf4a87152" title="Solve the SVM training problem.">solve</a>(</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>        random::rng_type&amp; rng,</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>        <span class="keywordtype">double</span> C,</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>        <a class="code hl_struct" href="structshark_1_1_qp_stopping_condition.html" title="stopping conditions for quadratic programming">QpStoppingCondition</a>&amp; stop,</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>        <a class="code hl_struct" href="structshark_1_1_qp_solution_properties.html" title="properties of the solution of a quadratic program">QpSolutionProperties</a>* prop = NULL,</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>        <span class="keywordtype">bool</span> verbose = <span class="keyword">false</span>)</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    {</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>        <span class="comment">// sanity checks</span></div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>        <a class="code hl_define" href="_exception_8h.html#a73abb5049a0168d72a48e72dda41708b">SHARK_ASSERT</a>(C &gt; 0.0);</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span> </div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>        <span class="comment">// measure training time</span></div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>        <a class="code hl_class" href="classshark_1_1_timer.html" title="Timer abstraction with microsecond resolution.">Timer</a> timer;</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>        timer.<a class="code hl_function" href="classshark_1_1_timer.html#a4d88aa872b2f0eb752c01c506cc24555" title="Stores the current time in m_startTime.">start</a>();</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span> </div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>        <span class="comment">// prepare dimensions and vectors</span></div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>        std::size_t ell = <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">m_data</a>.size();             <span class="comment">// number of training examples</span></div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>        RealMatrix alpha(ell, <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a> + 1, 0.0);   <span class="comment">// Lagrange multipliers; dual variables. Reserve one extra column.</span></div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>        RealMatrix w(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>, <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a04cb0e529976e34569d0b6863e36b881" title="input space dimension">m_dim</a>, 0.0);         <span class="comment">// weight vectors; primal variables</span></div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span> </div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>        <span class="comment">// scheduling of steps, for ACF only</span></div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>        RealVector pref(ell, 1.0);                   <span class="comment">// example-wise measure of success</span></div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>        <span class="keywordtype">double</span> prefsum = (double)ell;                <span class="comment">// normalization constant</span></div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span> </div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>        std::vector&lt;std::size_t&gt; schedule(ell);</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>        <span class="keywordflow">if</span> (<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab5489cad6b7a0db6065331414ae21dc7" title="strategy for coordinate selection">m_strategy</a> == <a class="code hl_enumvalue" href="classshark_1_1_qp_mc_linear.html#a844cac01d9113019e1f89de7d0810d79ac281d0b5f356d094aa5ad039e28cdc35">UNIFORM</a>)</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>        {</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>            <span class="keywordflow">for</span> (std::size_t i=0; i&lt;ell; i++) schedule[i] = i;</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>        }</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span> </div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>        <span class="comment">// used for shrinking</span></div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>        std::size_t active = ell;</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span> </div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>        <span class="comment">// prepare counters</span></div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>        std::size_t epoch = 0;</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>        std::size_t steps = 0;</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span> </div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>        <span class="comment">// prepare performance monitoring</span></div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>        <span class="keywordtype">double</span> objective = 0.0;</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>        <span class="keywordtype">double</span> max_violation = 0.0;</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span> </div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>        <span class="comment">// gain for ACF</span></div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>        <span class="keyword">const</span> <span class="keywordtype">double</span> gain_learning_rate = 1.0 / ell;</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>        <span class="keywordtype">double</span> average_gain = 0.0;</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span> </div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span> </div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span>        <span class="comment">// outer optimization loop (epochs)</span></div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>        <span class="keywordtype">bool</span> canstop = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>        <span class="keywordflow">while</span> (<span class="keyword">true</span>)</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>        {</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>            <span class="keywordflow">if</span> (<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab5489cad6b7a0db6065331414ae21dc7" title="strategy for coordinate selection">m_strategy</a> == <a class="code hl_enumvalue" href="classshark_1_1_qp_mc_linear.html#a844cac01d9113019e1f89de7d0810d79a306e16139b81caaa99ea79d3ede9a712">ACF</a>)</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>            {</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>                <span class="comment">// define schedule</span></div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>                <span class="keywordtype">double</span> psum = prefsum;</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>                prefsum = 0.0;</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span>                std::size_t pos = 0;</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>                <span class="keywordflow">for</span> (std::size_t i=0; i&lt;ell; i++)</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>                {</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>                    <span class="keywordtype">double</span> p = pref(i);</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>                    <span class="keywordtype">double</span> num = (psum &lt; 1e-6) ? ell - pos : std::min((<span class="keywordtype">double</span>)(ell - pos), (ell - pos) * p / psum);</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span>                    std::size_t n = (std::size_t)std::floor(num);</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>                    <span class="keywordtype">double</span> prob = num - n;</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>                    <span class="comment">//~ if (random::coinToss(rng,prob)) n++;</span></div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>                    <span class="keywordflow">if</span> (<a class="code hl_function" href="namespaceshark_1_1random.html#a18f302ea18f70835c59935973ba8ea84" title="Draws a number uniformly in [lower,upper] by drawing random numbers from rng.">random::uni</a>(rng) &lt; prob) n++;</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>                    <span class="keywordflow">for</span> (std::size_t j=0; j&lt;n; j++)</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>                    {</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>                        schedule[pos] = i;</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>                        pos++;</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>                    }</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>                    psum -= p;</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>                    prefsum += p;</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>                }</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>                <a class="code hl_define" href="_exception_8h.html#a73abb5049a0168d72a48e72dda41708b">SHARK_ASSERT</a>(pos == ell);</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>            }</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span> </div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>            <span class="keywordflow">if</span> (<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a4881e1ffbdb28a0f2d0fee00373e4e09" title="apply shrinking or not?">m_shrinking</a> == <span class="keyword">true</span>)</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>            {</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>                <span class="comment">//~ for (std::size_t i=0; i&lt;active; i++) </span></div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>                    <span class="comment">//~ std::swap(schedule[i], schedule[random::discrete(rng, std::size_t(0), active - 1)]);</span></div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>                std::shuffle(schedule.begin(),schedule.begin()+active,rng);</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>            }</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>            <span class="keywordflow">else</span></div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>            {</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>                <span class="comment">//~ for (std::size_t i=0; i&lt;ell; i++) </span></div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>                    <span class="comment">//~ std::swap(schedule[i], schedule[random::discrete(rng, std::size_t(0), ell - 1)]);</span></div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>                std::shuffle(schedule.begin(),schedule.end(),rng);</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>            }</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span> </div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>            <span class="comment">// inner loop (one epoch)</span></div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>            max_violation = 0.0;</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>            <span class="keywordtype">size_t</span> nPoints = ell;</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>            <span class="keywordflow">if</span> (<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a4881e1ffbdb28a0f2d0fee00373e4e09" title="apply shrinking or not?">m_shrinking</a> == <span class="keyword">true</span>)</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>                nPoints = active;</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span> </div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>            <span class="keywordflow">for</span> (std::size_t j=0; j&lt;nPoints; j++)</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>            {</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>                <span class="comment">// active example</span></div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>                <span class="keywordtype">double</span> gain = 0.0;</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>                <span class="keyword">const</span> std::size_t i = schedule[j];</div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>                <a class="code hl_typedef" href="classshark_1_1_qp_mc_linear.html#a88e09c2e6decd1e35f0755f0faf982f7">InputReferenceType</a> x_i = <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">m_data</a>[i].input;</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>                <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y_i = <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">m_data</a>[i].label;</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> q = <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#adb2a6e9f3681450a55dd5764648d0cb6" title="diagonal entries of the quadratic matrix">m_xSquared</a>(i);</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>                blas::dense_vector_adaptor&lt;double&gt; a = row(alpha, i);</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span> </div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>                <span class="comment">// compute gradient and KKT violation</span></div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>                RealVector wx = prod(w,x_i);</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>                RealVector g(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>);</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>                <span class="keywordtype">double</span> kkt = <a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#a6ff5650431f4502b6a76e7b79b7ff514" title="Compute the gradient from the inner products of the weight vectors with the current sample.">calcGradient</a>(g, wx, a, C, y_i);</div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span> </div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>                <span class="keywordflow">if</span> (kkt &gt; 0.0)</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>                {</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>                    max_violation = std::max(max_violation, kkt);</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span> </div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>                    <span class="comment">// perform the step on alpha</span></div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>                    RealVector mu(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>, 0.0);</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>                    gain = <a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#ad1bd9cdcfb10e5aca7c77e16812bae92" title="Solve the sub-problem posed by a single training example.">solveSub</a>(0.1 * stop.<a class="code hl_variable" href="structshark_1_1_qp_stopping_condition.html#addc2ea7f6d15eb25187586e329f33ace" title="minimum accuracy to be achieved, usually KKT violation">minAccuracy</a>, g, q, C, y_i, a, mu);</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>                    objective += gain;</div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>                    steps++;</div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span> </div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>                    <span class="comment">// update weight vectors</span></div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>                    <a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#addbaf611cbd58e4a4e3d07b80a95fbf4" title="Update the weight vectors (primal variables) after a step on the dual variables.">updateWeightVectors</a>(w, mu, i);</div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>                }</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>                <span class="keywordflow">else</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a4881e1ffbdb28a0f2d0fee00373e4e09" title="apply shrinking or not?">m_shrinking</a> == <span class="keyword">true</span>)</div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>                {</div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>                    active--;</div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>                    std::swap(schedule[j], schedule[active]);</div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>                    j--;</div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>                }</div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span> </div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>                <span class="comment">// update gain-based preferences</span></div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>                <span class="keywordflow">if</span> (<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab5489cad6b7a0db6065331414ae21dc7" title="strategy for coordinate selection">m_strategy</a> == <a class="code hl_enumvalue" href="classshark_1_1_qp_mc_linear.html#a844cac01d9113019e1f89de7d0810d79a306e16139b81caaa99ea79d3ede9a712">ACF</a>)</div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>                {</div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>                    <span class="keywordflow">if</span> (epoch == 0) average_gain += gain / (double)ell;</div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>                    <span class="keywordflow">else</span></div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>                    {</div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>                        <span class="comment">// strategy constants</span></div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>                        <span class="keyword">constexpr</span> <span class="keywordtype">double</span> CHANGE_RATE = 0.2;</div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>                        <span class="keyword">constexpr</span> <span class="keywordtype">double</span> PREF_MIN = 0.05;</div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>                        <span class="keyword">constexpr</span> <span class="keywordtype">double</span> PREF_MAX = 20.0;</div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span> </div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>                        <span class="keywordtype">double</span> change = CHANGE_RATE * (gain / average_gain - 1.0);</div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>                        <span class="keywordtype">double</span> newpref = std::min(PREF_MAX, std::max(PREF_MIN, pref(i) * std::exp(change)));</div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>                        prefsum += newpref - pref(i);</div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>                        pref(i) = newpref;</div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>                        average_gain = (1.0 - gain_learning_rate) * average_gain + gain_learning_rate * gain;</div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>                    }</div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>                }</div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>            }</div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span> </div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>            epoch++;</div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span> </div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>            <span class="comment">// stopping criteria</span></div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>            <span class="keywordflow">if</span> (stop.<a class="code hl_variable" href="structshark_1_1_qp_stopping_condition.html#af747ff263a208a610fc2ca4dccec44d6" title="maximum number of decomposition iterations (default to 0 - not used)">maxIterations</a> &gt; 0 &amp;&amp; epoch * ell &gt;= stop.<a class="code hl_variable" href="structshark_1_1_qp_stopping_condition.html#af747ff263a208a610fc2ca4dccec44d6" title="maximum number of decomposition iterations (default to 0 - not used)">maxIterations</a>)</div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>            {</div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>                <span class="keywordflow">if</span> (prop != NULL) prop-&gt;type = <a class="code hl_enumvalue" href="namespaceshark.html#a2d5e9a415ae7e8dd41caf883e1873540a1f2d9c58ed6b0985decbfe573d66080d">QpMaxIterationsReached</a>;</div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>                <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>            }</div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span> </div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>            <span class="keywordflow">if</span> (timer.<a class="code hl_function" href="classshark_1_1_timer.html#ad3ccd47c0429d28d9600117b5ed57362" title="Returns the difference between current time and the start time.">stop</a>() &gt;= stop.<a class="code hl_variable" href="structshark_1_1_qp_stopping_condition.html#a2f2037cc62c817ff88ec0801591a0240" title="maximum process time (defaults to 1e100 - not used)">maxSeconds</a>)</div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>            {</div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>                <span class="keywordflow">if</span> (prop != NULL) prop-&gt;type = <a class="code hl_enumvalue" href="namespaceshark.html#a2d5e9a415ae7e8dd41caf883e1873540af0f960c500ba6a3c653c9f45efa6e92a">QpTimeout</a>;</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>                <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>            }</div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span> </div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>            <span class="keywordflow">if</span> (max_violation &lt; stop.<a class="code hl_variable" href="structshark_1_1_qp_stopping_condition.html#addc2ea7f6d15eb25187586e329f33ace" title="minimum accuracy to be achieved, usually KKT violation">minAccuracy</a>)</div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>            {</div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>                <span class="keywordflow">if</span> (verbose)</div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span>                    std::cout &lt;&lt; <span class="stringliteral">&quot;#&quot;</span> &lt;&lt; std::flush;</div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>                <span class="keywordflow">if</span> (canstop)</div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>                {</div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>                    <span class="keywordflow">if</span> (prop != NULL) prop-&gt;type = <a class="code hl_enumvalue" href="namespaceshark.html#a2d5e9a415ae7e8dd41caf883e1873540a4b605bae89750d1c2bb1b3ef1a039639">QpAccuracyReached</a>;</div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span>                    <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>                }</div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>                <span class="keywordflow">else</span></div>
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>                {</div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>                    <span class="keywordflow">if</span> (<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab5489cad6b7a0db6065331414ae21dc7" title="strategy for coordinate selection">m_strategy</a> == <a class="code hl_enumvalue" href="classshark_1_1_qp_mc_linear.html#a844cac01d9113019e1f89de7d0810d79a306e16139b81caaa99ea79d3ede9a712">ACF</a>)</div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>                    {</div>
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>                        <span class="comment">// prepare full sweep for a reliable checking of the stopping criterion</span></div>
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>                        canstop = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>                        <span class="keywordflow">for</span> (std::size_t i=0; i&lt;ell; i++) pref(i) = 1.0;</div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span>                        prefsum = (double)ell;</div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>                    }</div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span> </div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>                    <span class="keywordflow">if</span> (<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a4881e1ffbdb28a0f2d0fee00373e4e09" title="apply shrinking or not?">m_shrinking</a> == <span class="keyword">true</span>)</div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>                    {</div>
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>                        <span class="comment">// prepare full sweep for a reliable checking of the stopping criterion</span></div>
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>                        active = ell;</div>
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>                        canstop = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>                    }</div>
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>                }</div>
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>            }</div>
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>            <span class="keywordflow">else</span></div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span>            {</div>
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span>                <span class="keywordflow">if</span> (verbose) std::cout &lt;&lt; <span class="stringliteral">&quot;.&quot;</span> &lt;&lt; std::flush;</div>
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>                <span class="keywordflow">if</span> (<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab5489cad6b7a0db6065331414ae21dc7" title="strategy for coordinate selection">m_strategy</a> == <a class="code hl_enumvalue" href="classshark_1_1_qp_mc_linear.html#a844cac01d9113019e1f89de7d0810d79a306e16139b81caaa99ea79d3ede9a712">ACF</a>)</div>
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span>                    canstop = <span class="keyword">false</span>;</div>
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span>                <span class="keywordflow">if</span> (<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a4881e1ffbdb28a0f2d0fee00373e4e09" title="apply shrinking or not?">m_shrinking</a> == <span class="keyword">true</span>)</div>
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span>                    canstop = (active == ell);</div>
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno">  300</span>            }</div>
<div class="line"><a id="l00301" name="l00301"></a><span class="lineno">  301</span>        }</div>
<div class="line"><a id="l00302" name="l00302"></a><span class="lineno">  302</span>        timer.<a class="code hl_function" href="classshark_1_1_timer.html#ad3ccd47c0429d28d9600117b5ed57362" title="Returns the difference between current time and the start time.">stop</a>();</div>
<div class="line"><a id="l00303" name="l00303"></a><span class="lineno">  303</span> </div>
<div class="line"><a id="l00304" name="l00304"></a><span class="lineno">  304</span>        <span class="comment">// calculate dual objective value</span></div>
<div class="line"><a id="l00305" name="l00305"></a><span class="lineno">  305</span>        objective = 0.0;</div>
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span>        <span class="keywordflow">for</span> (std::size_t j=0; j&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; j++)</div>
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span>        {</div>
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno">  308</span>            <span class="keywordflow">for</span> (std::size_t d=0; d&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a04cb0e529976e34569d0b6863e36b881" title="input space dimension">m_dim</a>; d++) objective -= w(j, d) * w(j, d);</div>
<div class="line"><a id="l00309" name="l00309"></a><span class="lineno">  309</span>        }</div>
<div class="line"><a id="l00310" name="l00310"></a><span class="lineno">  310</span>        objective *= 0.5;</div>
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno">  311</span>        <span class="keywordflow">for</span> (std::size_t i=0; i&lt;ell; i++)</div>
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno">  312</span>        {</div>
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno">  313</span>            <span class="keywordflow">for</span> (std::size_t j=0; j&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; j++) objective += alpha(i, j);</div>
<div class="line"><a id="l00314" name="l00314"></a><span class="lineno">  314</span>        }</div>
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno">  315</span> </div>
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno">  316</span>        <span class="comment">// return solution statistics</span></div>
<div class="line"><a id="l00317" name="l00317"></a><span class="lineno">  317</span>        <span class="keywordflow">if</span> (prop != NULL)</div>
<div class="line"><a id="l00318" name="l00318"></a><span class="lineno">  318</span>        {</div>
<div class="line"><a id="l00319" name="l00319"></a><span class="lineno">  319</span>            prop-&gt;accuracy = max_violation;       <span class="comment">// this is approximate, but a good guess</span></div>
<div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span>            prop-&gt;iterations = ell * epoch;</div>
<div class="line"><a id="l00321" name="l00321"></a><span class="lineno">  321</span>            prop-&gt;value = objective;</div>
<div class="line"><a id="l00322" name="l00322"></a><span class="lineno">  322</span>            prop-&gt;seconds = timer.<a class="code hl_function" href="classshark_1_1_timer.html#a91e2a527ffbe3eabc7c8cf36ff742318" title="Returns the last value of stop().">lastLap</a>();</div>
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span>        }</div>
<div class="line"><a id="l00324" name="l00324"></a><span class="lineno">  324</span> </div>
<div class="line"><a id="l00325" name="l00325"></a><span class="lineno">  325</span>        <span class="comment">// output solution statistics</span></div>
<div class="line"><a id="l00326" name="l00326"></a><span class="lineno">  326</span>        <span class="keywordflow">if</span> (verbose)</div>
<div class="line"><a id="l00327" name="l00327"></a><span class="lineno">  327</span>        {</div>
<div class="line"><a id="l00328" name="l00328"></a><span class="lineno">  328</span>            std::cout &lt;&lt; std::endl;</div>
<div class="line"><a id="l00329" name="l00329"></a><span class="lineno">  329</span>            std::cout &lt;&lt; <span class="stringliteral">&quot;training time (seconds): &quot;</span> &lt;&lt; timer.<a class="code hl_function" href="classshark_1_1_timer.html#a91e2a527ffbe3eabc7c8cf36ff742318" title="Returns the last value of stop().">lastLap</a>() &lt;&lt; std::endl;</div>
<div class="line"><a id="l00330" name="l00330"></a><span class="lineno">  330</span>            std::cout &lt;&lt; <span class="stringliteral">&quot;number of epochs: &quot;</span> &lt;&lt; epoch &lt;&lt; std::endl;</div>
<div class="line"><a id="l00331" name="l00331"></a><span class="lineno">  331</span>            std::cout &lt;&lt; <span class="stringliteral">&quot;number of iterations: &quot;</span> &lt;&lt; (ell * epoch) &lt;&lt; std::endl;</div>
<div class="line"><a id="l00332" name="l00332"></a><span class="lineno">  332</span>            std::cout &lt;&lt; <span class="stringliteral">&quot;number of non-zero steps: &quot;</span> &lt;&lt; steps &lt;&lt; std::endl;</div>
<div class="line"><a id="l00333" name="l00333"></a><span class="lineno">  333</span>            std::cout &lt;&lt; <span class="stringliteral">&quot;dual accuracy: &quot;</span> &lt;&lt; max_violation &lt;&lt; std::endl;</div>
<div class="line"><a id="l00334" name="l00334"></a><span class="lineno">  334</span>            std::cout &lt;&lt; <span class="stringliteral">&quot;dual objective value: &quot;</span> &lt;&lt; objective &lt;&lt; std::endl;</div>
<div class="line"><a id="l00335" name="l00335"></a><span class="lineno">  335</span>        }</div>
<div class="line"><a id="l00336" name="l00336"></a><span class="lineno">  336</span> </div>
<div class="line"><a id="l00337" name="l00337"></a><span class="lineno">  337</span>        <span class="comment">// return the solution</span></div>
<div class="line"><a id="l00338" name="l00338"></a><span class="lineno">  338</span>        <span class="keywordflow">return</span> w;</div>
<div class="line"><a id="l00339" name="l00339"></a><span class="lineno">  339</span>    }</div>
</div>
<div class="line"><a id="l00340" name="l00340"></a><span class="lineno">  340</span> </div>
<div class="line"><a id="l00341" name="l00341"></a><span class="lineno">  341</span><span class="keyword">protected</span>:</div>
<div class="line"><a id="l00342" name="l00342"></a><span class="lineno">  342</span>    <span class="comment">// for all c: row(w, c) += mu(c) * x</span></div>
<div class="foldopen" id="foldopen00343" data-start="{" data-end="}">
<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear.html#a64edc8279169777bf9ef05052a412acd">  343</a></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#a64edc8279169777bf9ef05052a412acd">add_scaled</a>(RealMatrix&amp; w, RealVector <span class="keyword">const</span>&amp; mu, <a class="code hl_typedef" href="classshark_1_1_qp_mc_linear.html#a88e09c2e6decd1e35f0755f0faf982f7">InputReferenceType</a> x)</div>
<div class="line"><a id="l00344" name="l00344"></a><span class="lineno">  344</span>    {</div>
<div class="line"><a id="l00345" name="l00345"></a><span class="lineno">  345</span>        <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) noalias(row(w, c)) += mu(c) * x;</div>
<div class="line"><a id="l00346" name="l00346"></a><span class="lineno">  346</span>    }</div>
</div>
<div class="line"><a id="l00347" name="l00347"></a><span class="lineno">  347</span><span class="comment"></span> </div>
<div class="line"><a id="l00348" name="l00348"></a><span class="lineno">  348</span><span class="comment">    /// \brief Compute the gradient from the inner products of the weight vectors with the current sample.</span></div>
<div class="line"><a id="l00349" name="l00349"></a><span class="lineno">  349</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00350" name="l00350"></a><span class="lineno">  350</span><span class="comment">    /// \param  gradient  gradient vector to be filled in. The vector is correctly sized.</span></div>
<div class="line"><a id="l00351" name="l00351"></a><span class="lineno">  351</span><span class="comment">    /// \param  wx        inner products of weight vectors with the current sample; wx(c) = &lt;w_c, x&gt;</span></div>
<div class="line"><a id="l00352" name="l00352"></a><span class="lineno">  352</span><span class="comment">    /// \param  alpha     variables corresponding to the current sample</span></div>
<div class="line"><a id="l00353" name="l00353"></a><span class="lineno">  353</span><span class="comment">    /// \param  C         upper bound on the variables</span></div>
<div class="line"><a id="l00354" name="l00354"></a><span class="lineno">  354</span><span class="comment">    /// \param  y         label of the current sample</span></div>
<div class="line"><a id="l00355" name="l00355"></a><span class="lineno">  355</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00356" name="l00356"></a><span class="lineno">  356</span><span class="comment">    /// \return  The function must return the violation of the KKT conditions.</span></div>
<div class="line"><a id="l00357" name="l00357"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear.html#a6ff5650431f4502b6a76e7b79b7ff514">  357</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#a6ff5650431f4502b6a76e7b79b7ff514" title="Compute the gradient from the inner products of the weight vectors with the current sample.">calcGradient</a>(RealVector&amp; gradient, RealVector wx, blas::dense_vector_adaptor&lt;double const&gt; <span class="keyword">const</span>&amp; alpha, <span class="keywordtype">double</span> C, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y) = 0;</div>
<div class="line"><a id="l00358" name="l00358"></a><span class="lineno">  358</span><span class="comment"></span> </div>
<div class="line"><a id="l00359" name="l00359"></a><span class="lineno">  359</span><span class="comment">    /// \brief Update the weight vectors (primal variables) after a step on the dual variables.</span></div>
<div class="line"><a id="l00360" name="l00360"></a><span class="lineno">  360</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00361" name="l00361"></a><span class="lineno">  361</span><span class="comment">    /// \param  w   matrix of (dense) weight vectors (as rows)</span></div>
<div class="line"><a id="l00362" name="l00362"></a><span class="lineno">  362</span><span class="comment">    /// \param  mu  dual step on the variables corresponding to the current sample</span></div>
<div class="line"><a id="l00363" name="l00363"></a><span class="lineno">  363</span><span class="comment">    /// \param  index   current sample</span></div>
<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear.html#addbaf611cbd58e4a4e3d07b80a95fbf4">  364</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#addbaf611cbd58e4a4e3d07b80a95fbf4" title="Update the weight vectors (primal variables) after a step on the dual variables.">updateWeightVectors</a>(RealMatrix&amp; w, RealVector <span class="keyword">const</span>&amp; mu, std::size_t index) = 0;</div>
<div class="line"><a id="l00365" name="l00365"></a><span class="lineno">  365</span><span class="comment"></span> </div>
<div class="line"><a id="l00366" name="l00366"></a><span class="lineno">  366</span><span class="comment">    /// \brief Solve the sub-problem posed by a single training example.</span></div>
<div class="line"><a id="l00367" name="l00367"></a><span class="lineno">  367</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00368" name="l00368"></a><span class="lineno">  368</span><span class="comment">    /// \param  epsilon   accuracy (dual gradient) up to which the sub-problem should be solved</span></div>
<div class="line"><a id="l00369" name="l00369"></a><span class="lineno">  369</span><span class="comment">    /// \param  gradient  gradient of the objective function w.r.t. alpha</span></div>
<div class="line"><a id="l00370" name="l00370"></a><span class="lineno">  370</span><span class="comment">    /// \param  q         squared norm of the current sample</span></div>
<div class="line"><a id="l00371" name="l00371"></a><span class="lineno">  371</span><span class="comment">    /// \param  C         upper bound on the variables</span></div>
<div class="line"><a id="l00372" name="l00372"></a><span class="lineno">  372</span><span class="comment">    /// \param  y         label of the current sample</span></div>
<div class="line"><a id="l00373" name="l00373"></a><span class="lineno">  373</span><span class="comment">    /// \param  alpha     input: initial point; output: (near) optimal point</span></div>
<div class="line"><a id="l00374" name="l00374"></a><span class="lineno">  374</span><span class="comment">    /// \param  mu        step from initial point to final point</span></div>
<div class="line"><a id="l00375" name="l00375"></a><span class="lineno">  375</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00376" name="l00376"></a><span class="lineno">  376</span><span class="comment">    /// \return  The function must return the gain of the step, i.e., the improvement of the objective function.</span></div>
<div class="line"><a id="l00377" name="l00377"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear.html#ad1bd9cdcfb10e5aca7c77e16812bae92">  377</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#ad1bd9cdcfb10e5aca7c77e16812bae92" title="Solve the sub-problem posed by a single training example.">solveSub</a>(<span class="keywordtype">double</span> epsilon, RealVector&amp; gradient, <span class="keywordtype">double</span> q, <span class="keywordtype">double</span> C, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y, blas::dense_vector_adaptor&lt;double&gt;&amp; alpha, RealVector&amp; mu) = 0;</div>
<div class="line"><a id="l00378" name="l00378"></a><span class="lineno">  378</span> </div>
<div class="line"><a id="l00379" name="l00379"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1">  379</a></span>    <a class="code hl_class" href="classshark_1_1_data_view.html" title="Constant time Element-Lookup for Datasets.">DataView&lt;const DatasetType&gt;</a> <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">m_data</a>;               <span class="comment">///&lt; view on training data</span></div>
<div class="line"><a id="l00380" name="l00380"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear.html#adb2a6e9f3681450a55dd5764648d0cb6">  380</a></span>    RealVector <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#adb2a6e9f3681450a55dd5764648d0cb6" title="diagonal entries of the quadratic matrix">m_xSquared</a>;                            <span class="comment">///&lt; diagonal entries of the quadratic matrix</span></div>
<div class="line"><a id="l00381" name="l00381"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear.html#a04cb0e529976e34569d0b6863e36b881">  381</a></span>    std::size_t <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a04cb0e529976e34569d0b6863e36b881" title="input space dimension">m_dim</a>;                                <span class="comment">///&lt; input space dimension</span></div>
<div class="line"><a id="l00382" name="l00382"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398">  382</a></span>    std::size_t <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;                            <span class="comment">///&lt; number of classes</span></div>
<div class="line"><a id="l00383" name="l00383"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear.html#ab5489cad6b7a0db6065331414ae21dc7">  383</a></span>    std::size_t <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab5489cad6b7a0db6065331414ae21dc7" title="strategy for coordinate selection">m_strategy</a>;                         <span class="comment">///&lt; strategy for coordinate selection</span></div>
<div class="line"><a id="l00384" name="l00384"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear.html#a4881e1ffbdb28a0f2d0fee00373e4e09">  384</a></span>    <span class="keywordtype">bool</span> <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a4881e1ffbdb28a0f2d0fee00373e4e09" title="apply shrinking or not?">m_shrinking</a>;                               <span class="comment">///&lt; apply shrinking or not?</span></div>
<div class="line"><a id="l00385" name="l00385"></a><span class="lineno">  385</span>};</div>
</div>
<div class="line"><a id="l00386" name="l00386"></a><span class="lineno">  386</span><span class="comment"></span> </div>
<div class="line"><a id="l00387" name="l00387"></a><span class="lineno">  387</span><span class="comment">/// \brief Solver for the multi-class SVM by Weston &amp; Watkins.</span></div>
<div class="line"><a id="l00388" name="l00388"></a><span class="lineno">  388</span><span class="comment"></span><span class="keyword">template</span> &lt;<span class="keyword">class</span> InputT&gt;</div>
<div class="foldopen" id="foldopen00389" data-start="{" data-end="};">
<div class="line"><a id="l00389" name="l00389"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_w_w.html">  389</a></span><span class="keyword">class </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear_w_w.html" title="Solver for the multi-class SVM by Weston &amp; Watkins.">QpMcLinearWW</a> : <span class="keyword">public</span> <a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;</div>
<div class="line"><a id="l00390" name="l00390"></a><span class="lineno">  390</span>{</div>
<div class="line"><a id="l00391" name="l00391"></a><span class="lineno">  391</span><span class="keyword">public</span>:</div>
<div class="line"><a id="l00392" name="l00392"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_w_w.html#aeab1965cb2ef7795e64e2949c8ec1089">  392</a></span>    <span class="keyword">typedef</span> <a class="code hl_class" href="classshark_1_1_labeled_data.html" title="Data set for supervised learning.">LabeledData&lt;InputT, unsigned int&gt;</a> <a class="code hl_typedef" href="classshark_1_1_qp_mc_linear_w_w.html#aeab1965cb2ef7795e64e2949c8ec1089">DatasetType</a>;</div>
<div class="line"><a id="l00393" name="l00393"></a><span class="lineno">  393</span><span class="comment"></span> </div>
<div class="line"><a id="l00394" name="l00394"></a><span class="lineno">  394</span><span class="comment">    /// \brief Constructor</span></div>
<div class="foldopen" id="foldopen00395" data-start="{" data-end="}">
<div class="line"><a id="l00395" name="l00395"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_w_w.html#ac41f4189c1fc9f6ea185bbe152cd88bb">  395</a></span><span class="comment"></span>    <a class="code hl_function" href="classshark_1_1_qp_mc_linear_w_w.html#ac41f4189c1fc9f6ea185bbe152cd88bb" title="Constructor.">QpMcLinearWW</a>(</div>
<div class="line"><a id="l00396" name="l00396"></a><span class="lineno">  396</span>            <span class="keyword">const</span> <a class="code hl_class" href="classshark_1_1_labeled_data.html" title="Data set for supervised learning.">DatasetType</a>&amp; dataset,</div>
<div class="line"><a id="l00397" name="l00397"></a><span class="lineno">  397</span>            std::size_t dim,</div>
<div class="line"><a id="l00398" name="l00398"></a><span class="lineno">  398</span>            std::size_t classes)</div>
<div class="line"><a id="l00399" name="l00399"></a><span class="lineno">  399</span>    : <a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;(dataset, dim, classes)</div>
<div class="line"><a id="l00400" name="l00400"></a><span class="lineno">  400</span>    { }</div>
</div>
<div class="line"><a id="l00401" name="l00401"></a><span class="lineno">  401</span> </div>
<div class="line"><a id="l00402" name="l00402"></a><span class="lineno">  402</span><span class="keyword">protected</span>:<span class="comment"></span></div>
<div class="line"><a id="l00403" name="l00403"></a><span class="lineno">  403</span><span class="comment">    /// \brief Compute the gradient from the inner products of the weight vectors with the current sample.</span></div>
<div class="foldopen" id="foldopen00404" data-start="{" data-end="}">
<div class="line"><a id="l00404" name="l00404"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_w_w.html#a229d689f6acbd6074b047fea92f90ce3">  404</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_w_w.html#a229d689f6acbd6074b047fea92f90ce3" title="Compute the gradient from the inner products of the weight vectors with the current sample.">calcGradient</a>(RealVector&amp; gradient, RealVector wx, blas::dense_vector_adaptor&lt;double const&gt; <span class="keyword">const</span>&amp; alpha, <span class="keywordtype">double</span> C, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y)</div>
<div class="line"><a id="l00405" name="l00405"></a><span class="lineno">  405</span>    {</div>
<div class="line"><a id="l00406" name="l00406"></a><span class="lineno">  406</span>        <span class="keywordtype">double</span> violation = 0.0;</div>
<div class="line"><a id="l00407" name="l00407"></a><span class="lineno">  407</span>        <span class="keywordflow">for</span> (std::size_t c=0; c&lt;wx.size(); c++)</div>
<div class="line"><a id="l00408" name="l00408"></a><span class="lineno">  408</span>        {</div>
<div class="line"><a id="l00409" name="l00409"></a><span class="lineno">  409</span>            <span class="keywordflow">if</span> (c == y)</div>
<div class="line"><a id="l00410" name="l00410"></a><span class="lineno">  410</span>            {</div>
<div class="line"><a id="l00411" name="l00411"></a><span class="lineno">  411</span>                gradient(c) = 0.0;</div>
<div class="line"><a id="l00412" name="l00412"></a><span class="lineno">  412</span>            }</div>
<div class="line"><a id="l00413" name="l00413"></a><span class="lineno">  413</span>            <span class="keywordflow">else</span></div>
<div class="line"><a id="l00414" name="l00414"></a><span class="lineno">  414</span>            {</div>
<div class="line"><a id="l00415" name="l00415"></a><span class="lineno">  415</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> g = 1.0 - 0.5 * (wx(y) - wx(c));</div>
<div class="line"><a id="l00416" name="l00416"></a><span class="lineno">  416</span>                gradient(c) = g;</div>
<div class="line"><a id="l00417" name="l00417"></a><span class="lineno">  417</span>                <span class="keywordflow">if</span> (g &gt; violation &amp;&amp; alpha(c) &lt; C) violation = g;</div>
<div class="line"><a id="l00418" name="l00418"></a><span class="lineno">  418</span>                <span class="keywordflow">else</span> <span class="keywordflow">if</span> (-g &gt; violation &amp;&amp; alpha(c) &gt; 0.0) violation = -g;</div>
<div class="line"><a id="l00419" name="l00419"></a><span class="lineno">  419</span>            }</div>
<div class="line"><a id="l00420" name="l00420"></a><span class="lineno">  420</span>        }</div>
<div class="line"><a id="l00421" name="l00421"></a><span class="lineno">  421</span>        <span class="keywordflow">return</span> violation;</div>
<div class="line"><a id="l00422" name="l00422"></a><span class="lineno">  422</span>    }</div>
</div>
<div class="line"><a id="l00423" name="l00423"></a><span class="lineno">  423</span><span class="comment"></span> </div>
<div class="line"><a id="l00424" name="l00424"></a><span class="lineno">  424</span><span class="comment">    /// \brief Update the weight vectors (primal variables) after a step on the dual variables.</span></div>
<div class="foldopen" id="foldopen00425" data-start="{" data-end="}">
<div class="line"><a id="l00425" name="l00425"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_w_w.html#a2a6f6e6036ecf905606e62db0dc3816a">  425</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_w_w.html#a2a6f6e6036ecf905606e62db0dc3816a" title="Update the weight vectors (primal variables) after a step on the dual variables.">updateWeightVectors</a>(RealMatrix&amp; w, RealVector <span class="keyword">const</span>&amp; mu, std::size_t index)</div>
<div class="line"><a id="l00426" name="l00426"></a><span class="lineno">  426</span>    {</div>
<div class="line"><a id="l00427" name="l00427"></a><span class="lineno">  427</span>        <span class="keywordtype">double</span> sum_mu = 0.0;</div>
<div class="line"><a id="l00428" name="l00428"></a><span class="lineno">  428</span>        <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) sum_mu += mu(c);</div>
<div class="line"><a id="l00429" name="l00429"></a><span class="lineno">  429</span>        <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y = <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">m_data</a>[index].label;</div>
<div class="line"><a id="l00430" name="l00430"></a><span class="lineno">  430</span>        RealVector step(-0.5 * mu);</div>
<div class="line"><a id="l00431" name="l00431"></a><span class="lineno">  431</span>        step(y) = 0.5 * sum_mu;</div>
<div class="line"><a id="l00432" name="l00432"></a><span class="lineno">  432</span>        <a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#a64edc8279169777bf9ef05052a412acd">add_scaled</a>(w, step, <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">m_data</a>[index].input);</div>
<div class="line"><a id="l00433" name="l00433"></a><span class="lineno">  433</span>    }</div>
</div>
<div class="line"><a id="l00434" name="l00434"></a><span class="lineno">  434</span><span class="comment"></span> </div>
<div class="line"><a id="l00435" name="l00435"></a><span class="lineno">  435</span><span class="comment">    /// \brief Solve the sub-problem posed by a single training example.</span></div>
<div class="foldopen" id="foldopen00436" data-start="{" data-end="}">
<div class="line"><a id="l00436" name="l00436"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_w_w.html#ac24ff73630263bee2b552222196d7ca6">  436</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_w_w.html#ac24ff73630263bee2b552222196d7ca6" title="Solve the sub-problem posed by a single training example.">solveSub</a>(<span class="keywordtype">double</span> epsilon, RealVector&amp; gradient, <span class="keywordtype">double</span> q, <span class="keywordtype">double</span> C, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y, blas::dense_vector_adaptor&lt;double&gt;&amp; alpha, RealVector&amp; mu)</div>
<div class="line"><a id="l00437" name="l00437"></a><span class="lineno">  437</span>    {</div>
<div class="line"><a id="l00438" name="l00438"></a><span class="lineno">  438</span>        <span class="keyword">const</span> <span class="keywordtype">double</span> qq = 0.5 * q;</div>
<div class="line"><a id="l00439" name="l00439"></a><span class="lineno">  439</span>        <span class="keywordtype">double</span> gain = 0.0;</div>
<div class="line"><a id="l00440" name="l00440"></a><span class="lineno">  440</span> </div>
<div class="line"><a id="l00441" name="l00441"></a><span class="lineno">  441</span>        <span class="comment">// SMO loop</span></div>
<div class="line"><a id="l00442" name="l00442"></a><span class="lineno">  442</span>        <span class="keywordtype">size_t</span> iter, maxiter = 10 * <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l00443" name="l00443"></a><span class="lineno">  443</span>        <span class="keywordflow">for</span> (iter=0; iter&lt;maxiter; iter++)</div>
<div class="line"><a id="l00444" name="l00444"></a><span class="lineno">  444</span>        {</div>
<div class="line"><a id="l00445" name="l00445"></a><span class="lineno">  445</span>            <span class="comment">// select working set</span></div>
<div class="line"><a id="l00446" name="l00446"></a><span class="lineno">  446</span>            std::size_t idx = 0;</div>
<div class="line"><a id="l00447" name="l00447"></a><span class="lineno">  447</span>            <span class="keywordtype">double</span> kkt = 0.0;</div>
<div class="line"><a id="l00448" name="l00448"></a><span class="lineno">  448</span>            <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++)</div>
<div class="line"><a id="l00449" name="l00449"></a><span class="lineno">  449</span>            {</div>
<div class="line"><a id="l00450" name="l00450"></a><span class="lineno">  450</span>                <span class="keywordflow">if</span> (c == y) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00451" name="l00451"></a><span class="lineno">  451</span> </div>
<div class="line"><a id="l00452" name="l00452"></a><span class="lineno">  452</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> g = gradient(c);</div>
<div class="line"><a id="l00453" name="l00453"></a><span class="lineno">  453</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> a = alpha(c);</div>
<div class="line"><a id="l00454" name="l00454"></a><span class="lineno">  454</span>                <span class="keywordflow">if</span> (g &gt; kkt &amp;&amp; a &lt; C) { kkt = g; idx = c; }</div>
<div class="line"><a id="l00455" name="l00455"></a><span class="lineno">  455</span>                <span class="keywordflow">else</span> <span class="keywordflow">if</span> (-g &gt; kkt &amp;&amp; a &gt; 0.0) { kkt = -g; idx = c; }</div>
<div class="line"><a id="l00456" name="l00456"></a><span class="lineno">  456</span>            }</div>
<div class="line"><a id="l00457" name="l00457"></a><span class="lineno">  457</span> </div>
<div class="line"><a id="l00458" name="l00458"></a><span class="lineno">  458</span>            <span class="comment">// check stopping criterion</span></div>
<div class="line"><a id="l00459" name="l00459"></a><span class="lineno">  459</span>            <span class="keywordflow">if</span> (kkt &lt; epsilon) <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00460" name="l00460"></a><span class="lineno">  460</span> </div>
<div class="line"><a id="l00461" name="l00461"></a><span class="lineno">  461</span>            <span class="comment">// perform step</span></div>
<div class="line"><a id="l00462" name="l00462"></a><span class="lineno">  462</span>            <span class="keyword">const</span> <span class="keywordtype">double</span> a = alpha(idx);</div>
<div class="line"><a id="l00463" name="l00463"></a><span class="lineno">  463</span>            <span class="keyword">const</span> <span class="keywordtype">double</span> g = gradient(idx);</div>
<div class="line"><a id="l00464" name="l00464"></a><span class="lineno">  464</span>            <span class="keywordtype">double</span> m = g / qq;</div>
<div class="line"><a id="l00465" name="l00465"></a><span class="lineno">  465</span>            <span class="keywordtype">double</span> a_new = a + m;</div>
<div class="line"><a id="l00466" name="l00466"></a><span class="lineno">  466</span>            <span class="keywordflow">if</span> (a_new &lt;= 0.0)</div>
<div class="line"><a id="l00467" name="l00467"></a><span class="lineno">  467</span>            {</div>
<div class="line"><a id="l00468" name="l00468"></a><span class="lineno">  468</span>                m = -a;</div>
<div class="line"><a id="l00469" name="l00469"></a><span class="lineno">  469</span>                a_new = 0.0;</div>
<div class="line"><a id="l00470" name="l00470"></a><span class="lineno">  470</span>            }</div>
<div class="line"><a id="l00471" name="l00471"></a><span class="lineno">  471</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (a_new &gt;= C)</div>
<div class="line"><a id="l00472" name="l00472"></a><span class="lineno">  472</span>            {</div>
<div class="line"><a id="l00473" name="l00473"></a><span class="lineno">  473</span>                m = C - a;</div>
<div class="line"><a id="l00474" name="l00474"></a><span class="lineno">  474</span>                a_new = C;</div>
<div class="line"><a id="l00475" name="l00475"></a><span class="lineno">  475</span>            }</div>
<div class="line"><a id="l00476" name="l00476"></a><span class="lineno">  476</span>            alpha(idx) = a_new;</div>
<div class="line"><a id="l00477" name="l00477"></a><span class="lineno">  477</span>            mu(idx) += m;</div>
<div class="line"><a id="l00478" name="l00478"></a><span class="lineno">  478</span> </div>
<div class="line"><a id="l00479" name="l00479"></a><span class="lineno">  479</span>            <span class="comment">// update gradient and total gain</span></div>
<div class="line"><a id="l00480" name="l00480"></a><span class="lineno">  480</span>            <span class="keyword">const</span> <span class="keywordtype">double</span> dg = 0.5 * m * qq;</div>
<div class="line"><a id="l00481" name="l00481"></a><span class="lineno">  481</span>            <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) gradient(c) -= dg;</div>
<div class="line"><a id="l00482" name="l00482"></a><span class="lineno">  482</span>            gradient(idx) -= dg;</div>
<div class="line"><a id="l00483" name="l00483"></a><span class="lineno">  483</span> </div>
<div class="line"><a id="l00484" name="l00484"></a><span class="lineno">  484</span>            gain += m * (g - dg);</div>
<div class="line"><a id="l00485" name="l00485"></a><span class="lineno">  485</span>        }</div>
<div class="line"><a id="l00486" name="l00486"></a><span class="lineno">  486</span> </div>
<div class="line"><a id="l00487" name="l00487"></a><span class="lineno">  487</span>        <span class="keywordflow">return</span> gain;</div>
<div class="line"><a id="l00488" name="l00488"></a><span class="lineno">  488</span>    }</div>
</div>
<div class="line"><a id="l00489" name="l00489"></a><span class="lineno">  489</span> </div>
<div class="line"><a id="l00490" name="l00490"></a><span class="lineno">  490</span><span class="keyword">protected</span>:</div>
<div class="line"><a id="l00491" name="l00491"></a><span class="lineno">  491</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#a64edc8279169777bf9ef05052a412acd">::add_scaled</a>;</div>
<div class="line"><a id="l00492" name="l00492"></a><span class="lineno">  492</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">::m_data</a>;</div>
<div class="line"><a id="l00493" name="l00493"></a><span class="lineno">  493</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">::m_classes</a>;</div>
<div class="line"><a id="l00494" name="l00494"></a><span class="lineno">  494</span>};</div>
</div>
<div class="line"><a id="l00495" name="l00495"></a><span class="lineno">  495</span> </div>
<div class="line"><a id="l00496" name="l00496"></a><span class="lineno">  496</span><span class="comment"></span> </div>
<div class="line"><a id="l00497" name="l00497"></a><span class="lineno">  497</span><span class="comment">/// \brief Solver for the multi-class SVM by Lee, Lin &amp; Wahba.</span></div>
<div class="line"><a id="l00498" name="l00498"></a><span class="lineno">  498</span><span class="comment"></span><span class="keyword">template</span> &lt;<span class="keyword">class</span> InputT&gt;</div>
<div class="foldopen" id="foldopen00499" data-start="{" data-end="};">
<div class="line"><a id="l00499" name="l00499"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_l_l_w.html">  499</a></span><span class="keyword">class </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear_l_l_w.html" title="Solver for the multi-class SVM by Lee, Lin &amp; Wahba.">QpMcLinearLLW</a> : <span class="keyword">public</span> <a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;</div>
<div class="line"><a id="l00500" name="l00500"></a><span class="lineno">  500</span>{</div>
<div class="line"><a id="l00501" name="l00501"></a><span class="lineno">  501</span><span class="keyword">public</span>:</div>
<div class="line"><a id="l00502" name="l00502"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_l_l_w.html#aaaf325364d5232e671602d914ef03f61">  502</a></span>    <span class="keyword">typedef</span> <a class="code hl_class" href="classshark_1_1_labeled_data.html" title="Data set for supervised learning.">LabeledData&lt;InputT, unsigned int&gt;</a> <a class="code hl_typedef" href="classshark_1_1_qp_mc_linear_l_l_w.html#aaaf325364d5232e671602d914ef03f61">DatasetType</a>;</div>
<div class="line"><a id="l00503" name="l00503"></a><span class="lineno">  503</span><span class="comment"></span> </div>
<div class="line"><a id="l00504" name="l00504"></a><span class="lineno">  504</span><span class="comment">    /// \brief Constructor</span></div>
<div class="foldopen" id="foldopen00505" data-start="{" data-end="}">
<div class="line"><a id="l00505" name="l00505"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_l_l_w.html#a6c65ffa1852f11ca67f8d819dd383756">  505</a></span><span class="comment"></span>    <a class="code hl_function" href="classshark_1_1_qp_mc_linear_l_l_w.html#a6c65ffa1852f11ca67f8d819dd383756" title="Constructor.">QpMcLinearLLW</a>(</div>
<div class="line"><a id="l00506" name="l00506"></a><span class="lineno">  506</span>            <span class="keyword">const</span> <a class="code hl_class" href="classshark_1_1_labeled_data.html" title="Data set for supervised learning.">DatasetType</a>&amp; dataset,</div>
<div class="line"><a id="l00507" name="l00507"></a><span class="lineno">  507</span>            std::size_t dim,</div>
<div class="line"><a id="l00508" name="l00508"></a><span class="lineno">  508</span>            std::size_t classes)</div>
<div class="line"><a id="l00509" name="l00509"></a><span class="lineno">  509</span>    : <a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;(dataset, dim, classes)</div>
<div class="line"><a id="l00510" name="l00510"></a><span class="lineno">  510</span>    { }</div>
</div>
<div class="line"><a id="l00511" name="l00511"></a><span class="lineno">  511</span> </div>
<div class="line"><a id="l00512" name="l00512"></a><span class="lineno">  512</span><span class="keyword">protected</span>:<span class="comment"></span></div>
<div class="line"><a id="l00513" name="l00513"></a><span class="lineno">  513</span><span class="comment">    /// \brief Compute the gradient from the inner products of the weight vectors with the current sample.</span></div>
<div class="foldopen" id="foldopen00514" data-start="{" data-end="}">
<div class="line"><a id="l00514" name="l00514"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_l_l_w.html#a5d36501d3f63730064d4439657bcb21f">  514</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_l_l_w.html#a5d36501d3f63730064d4439657bcb21f" title="Compute the gradient from the inner products of the weight vectors with the current sample.">calcGradient</a>(RealVector&amp; gradient, RealVector wx, blas::dense_vector_adaptor&lt;double const&gt; <span class="keyword">const</span>&amp; alpha, <span class="keywordtype">double</span> C, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y)</div>
<div class="line"><a id="l00515" name="l00515"></a><span class="lineno">  515</span>    {</div>
<div class="line"><a id="l00516" name="l00516"></a><span class="lineno">  516</span>        <span class="keywordtype">double</span> violation = 0.0;</div>
<div class="line"><a id="l00517" name="l00517"></a><span class="lineno">  517</span>        <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++)</div>
<div class="line"><a id="l00518" name="l00518"></a><span class="lineno">  518</span>        {</div>
<div class="line"><a id="l00519" name="l00519"></a><span class="lineno">  519</span>            <span class="keywordflow">if</span> (c == y)</div>
<div class="line"><a id="l00520" name="l00520"></a><span class="lineno">  520</span>            {</div>
<div class="line"><a id="l00521" name="l00521"></a><span class="lineno">  521</span>                gradient(c) = 0.0;</div>
<div class="line"><a id="l00522" name="l00522"></a><span class="lineno">  522</span>            }</div>
<div class="line"><a id="l00523" name="l00523"></a><span class="lineno">  523</span>            <span class="keywordflow">else</span></div>
<div class="line"><a id="l00524" name="l00524"></a><span class="lineno">  524</span>            {</div>
<div class="line"><a id="l00525" name="l00525"></a><span class="lineno">  525</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> g = 1.0 + wx(c);</div>
<div class="line"><a id="l00526" name="l00526"></a><span class="lineno">  526</span>                gradient(c) = g;</div>
<div class="line"><a id="l00527" name="l00527"></a><span class="lineno">  527</span>                <span class="keywordflow">if</span> (g &gt; violation &amp;&amp; alpha(c) &lt; C) violation = g;</div>
<div class="line"><a id="l00528" name="l00528"></a><span class="lineno">  528</span>                <span class="keywordflow">else</span> <span class="keywordflow">if</span> (-g &gt; violation &amp;&amp; alpha(c) &gt; 0.0) violation = -g;</div>
<div class="line"><a id="l00529" name="l00529"></a><span class="lineno">  529</span>            }</div>
<div class="line"><a id="l00530" name="l00530"></a><span class="lineno">  530</span>        }</div>
<div class="line"><a id="l00531" name="l00531"></a><span class="lineno">  531</span>        <span class="keywordflow">return</span> violation;</div>
<div class="line"><a id="l00532" name="l00532"></a><span class="lineno">  532</span>    }</div>
</div>
<div class="line"><a id="l00533" name="l00533"></a><span class="lineno">  533</span><span class="comment"></span> </div>
<div class="line"><a id="l00534" name="l00534"></a><span class="lineno">  534</span><span class="comment">    /// \brief Update the weight vectors (primal variables) after a step on the dual variables.</span></div>
<div class="foldopen" id="foldopen00535" data-start="{" data-end="}">
<div class="line"><a id="l00535" name="l00535"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_l_l_w.html#a9c312d2e29afc1323b24d84ca390d2c0">  535</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_l_l_w.html#a9c312d2e29afc1323b24d84ca390d2c0" title="Update the weight vectors (primal variables) after a step on the dual variables.">updateWeightVectors</a>(RealMatrix&amp; w, RealVector <span class="keyword">const</span>&amp; mu, std::size_t index)</div>
<div class="line"><a id="l00536" name="l00536"></a><span class="lineno">  536</span>    {</div>
<div class="line"><a id="l00537" name="l00537"></a><span class="lineno">  537</span>        <span class="keywordtype">double</span> mean_mu = 0.0;</div>
<div class="line"><a id="l00538" name="l00538"></a><span class="lineno">  538</span>        <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) mean_mu += mu(c);</div>
<div class="line"><a id="l00539" name="l00539"></a><span class="lineno">  539</span>        mean_mu /= (double)<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l00540" name="l00540"></a><span class="lineno">  540</span>        RealVector step(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>);</div>
<div class="line"><a id="l00541" name="l00541"></a><span class="lineno">  541</span>        <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) step(c) = mean_mu - mu(c);</div>
<div class="line"><a id="l00542" name="l00542"></a><span class="lineno">  542</span>        <a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#a64edc8279169777bf9ef05052a412acd">add_scaled</a>(w, step, <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">m_data</a>[index].input);</div>
<div class="line"><a id="l00543" name="l00543"></a><span class="lineno">  543</span>    }</div>
</div>
<div class="line"><a id="l00544" name="l00544"></a><span class="lineno">  544</span><span class="comment"></span> </div>
<div class="line"><a id="l00545" name="l00545"></a><span class="lineno">  545</span><span class="comment">    /// \brief Solve the sub-problem posed by a single training example.</span></div>
<div class="foldopen" id="foldopen00546" data-start="{" data-end="}">
<div class="line"><a id="l00546" name="l00546"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_l_l_w.html#a5d146ba6191a078d4d02ef0f385c1f66">  546</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_l_l_w.html#a5d146ba6191a078d4d02ef0f385c1f66" title="Solve the sub-problem posed by a single training example.">solveSub</a>(<span class="keywordtype">double</span> epsilon, RealVector&amp; gradient, <span class="keywordtype">double</span> q, <span class="keywordtype">double</span> C, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y, blas::dense_vector_adaptor&lt;double&gt;&amp; alpha, RealVector&amp; mu)</div>
<div class="line"><a id="l00547" name="l00547"></a><span class="lineno">  547</span>    {</div>
<div class="line"><a id="l00548" name="l00548"></a><span class="lineno">  548</span>        <span class="keyword">const</span> <span class="keywordtype">double</span> ood = 1.0 / <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l00549" name="l00549"></a><span class="lineno">  549</span>        <span class="keyword">const</span> <span class="keywordtype">double</span> qq = (1.0 - ood) * q;</div>
<div class="line"><a id="l00550" name="l00550"></a><span class="lineno">  550</span>        <span class="keywordtype">double</span> gain = 0.0;</div>
<div class="line"><a id="l00551" name="l00551"></a><span class="lineno">  551</span> </div>
<div class="line"><a id="l00552" name="l00552"></a><span class="lineno">  552</span>        <span class="comment">// SMO loop</span></div>
<div class="line"><a id="l00553" name="l00553"></a><span class="lineno">  553</span>        <span class="keywordtype">size_t</span> iter, maxiter = 10 * <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l00554" name="l00554"></a><span class="lineno">  554</span>        <span class="keywordflow">for</span> (iter=0; iter&lt;maxiter; iter++)</div>
<div class="line"><a id="l00555" name="l00555"></a><span class="lineno">  555</span>        {</div>
<div class="line"><a id="l00556" name="l00556"></a><span class="lineno">  556</span>            <span class="comment">// select working set</span></div>
<div class="line"><a id="l00557" name="l00557"></a><span class="lineno">  557</span>            std::size_t idx = 0;</div>
<div class="line"><a id="l00558" name="l00558"></a><span class="lineno">  558</span>            <span class="keywordtype">double</span> kkt = 0.0;</div>
<div class="line"><a id="l00559" name="l00559"></a><span class="lineno">  559</span>            <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++)</div>
<div class="line"><a id="l00560" name="l00560"></a><span class="lineno">  560</span>            {</div>
<div class="line"><a id="l00561" name="l00561"></a><span class="lineno">  561</span>                <span class="keywordflow">if</span> (c == y) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00562" name="l00562"></a><span class="lineno">  562</span> </div>
<div class="line"><a id="l00563" name="l00563"></a><span class="lineno">  563</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> g = gradient(c);</div>
<div class="line"><a id="l00564" name="l00564"></a><span class="lineno">  564</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> a = alpha(c);</div>
<div class="line"><a id="l00565" name="l00565"></a><span class="lineno">  565</span>                <span class="keywordflow">if</span> (g &gt; kkt &amp;&amp; a &lt; C) { kkt = g; idx = c; }</div>
<div class="line"><a id="l00566" name="l00566"></a><span class="lineno">  566</span>                <span class="keywordflow">else</span> <span class="keywordflow">if</span> (-g &gt; kkt &amp;&amp; a &gt; 0.0) { kkt = -g; idx = c; }</div>
<div class="line"><a id="l00567" name="l00567"></a><span class="lineno">  567</span>            }</div>
<div class="line"><a id="l00568" name="l00568"></a><span class="lineno">  568</span> </div>
<div class="line"><a id="l00569" name="l00569"></a><span class="lineno">  569</span>            <span class="comment">// check stopping criterion</span></div>
<div class="line"><a id="l00570" name="l00570"></a><span class="lineno">  570</span>            <span class="keywordflow">if</span> (kkt &lt; epsilon) <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00571" name="l00571"></a><span class="lineno">  571</span> </div>
<div class="line"><a id="l00572" name="l00572"></a><span class="lineno">  572</span>            <span class="comment">// perform step</span></div>
<div class="line"><a id="l00573" name="l00573"></a><span class="lineno">  573</span>            <span class="keyword">const</span> <span class="keywordtype">double</span> a = alpha(idx);</div>
<div class="line"><a id="l00574" name="l00574"></a><span class="lineno">  574</span>            <span class="keyword">const</span> <span class="keywordtype">double</span> g = gradient(idx);</div>
<div class="line"><a id="l00575" name="l00575"></a><span class="lineno">  575</span>            <span class="keywordtype">double</span> m = g / qq;</div>
<div class="line"><a id="l00576" name="l00576"></a><span class="lineno">  576</span>            <span class="keywordtype">double</span> a_new = a + m;</div>
<div class="line"><a id="l00577" name="l00577"></a><span class="lineno">  577</span>            <span class="keywordflow">if</span> (a_new &lt;= 0.0)</div>
<div class="line"><a id="l00578" name="l00578"></a><span class="lineno">  578</span>            {</div>
<div class="line"><a id="l00579" name="l00579"></a><span class="lineno">  579</span>                m = -a;</div>
<div class="line"><a id="l00580" name="l00580"></a><span class="lineno">  580</span>                a_new = 0.0;</div>
<div class="line"><a id="l00581" name="l00581"></a><span class="lineno">  581</span>            }</div>
<div class="line"><a id="l00582" name="l00582"></a><span class="lineno">  582</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (a_new &gt;= C)</div>
<div class="line"><a id="l00583" name="l00583"></a><span class="lineno">  583</span>            {</div>
<div class="line"><a id="l00584" name="l00584"></a><span class="lineno">  584</span>                m = C - a;</div>
<div class="line"><a id="l00585" name="l00585"></a><span class="lineno">  585</span>                a_new = C;</div>
<div class="line"><a id="l00586" name="l00586"></a><span class="lineno">  586</span>            }</div>
<div class="line"><a id="l00587" name="l00587"></a><span class="lineno">  587</span>            alpha(idx) = a_new;</div>
<div class="line"><a id="l00588" name="l00588"></a><span class="lineno">  588</span>            mu(idx) += m;</div>
<div class="line"><a id="l00589" name="l00589"></a><span class="lineno">  589</span> </div>
<div class="line"><a id="l00590" name="l00590"></a><span class="lineno">  590</span>            <span class="comment">// update gradient and total gain</span></div>
<div class="line"><a id="l00591" name="l00591"></a><span class="lineno">  591</span>            <span class="keyword">const</span> <span class="keywordtype">double</span> dg = m * q;</div>
<div class="line"><a id="l00592" name="l00592"></a><span class="lineno">  592</span>            <span class="keyword">const</span> <span class="keywordtype">double</span> dgc = dg / <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l00593" name="l00593"></a><span class="lineno">  593</span>            <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) gradient(c) += dgc;</div>
<div class="line"><a id="l00594" name="l00594"></a><span class="lineno">  594</span>            gradient(idx) -= dg;</div>
<div class="line"><a id="l00595" name="l00595"></a><span class="lineno">  595</span> </div>
<div class="line"><a id="l00596" name="l00596"></a><span class="lineno">  596</span>            gain += m * (g - 0.5 * (dg - dgc));</div>
<div class="line"><a id="l00597" name="l00597"></a><span class="lineno">  597</span>        }</div>
<div class="line"><a id="l00598" name="l00598"></a><span class="lineno">  598</span> </div>
<div class="line"><a id="l00599" name="l00599"></a><span class="lineno">  599</span>        <span class="keywordflow">return</span> gain;</div>
<div class="line"><a id="l00600" name="l00600"></a><span class="lineno">  600</span>    }</div>
</div>
<div class="line"><a id="l00601" name="l00601"></a><span class="lineno">  601</span> </div>
<div class="line"><a id="l00602" name="l00602"></a><span class="lineno">  602</span><span class="keyword">protected</span>:</div>
<div class="line"><a id="l00603" name="l00603"></a><span class="lineno">  603</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#a64edc8279169777bf9ef05052a412acd">::add_scaled</a>;</div>
<div class="line"><a id="l00604" name="l00604"></a><span class="lineno">  604</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">::m_data</a>;</div>
<div class="line"><a id="l00605" name="l00605"></a><span class="lineno">  605</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">::m_classes</a>;</div>
<div class="line"><a id="l00606" name="l00606"></a><span class="lineno">  606</span>};</div>
</div>
<div class="line"><a id="l00607" name="l00607"></a><span class="lineno">  607</span> </div>
<div class="line"><a id="l00608" name="l00608"></a><span class="lineno">  608</span><span class="comment"></span> </div>
<div class="line"><a id="l00609" name="l00609"></a><span class="lineno">  609</span><span class="comment">/// \brief Solver for the multi-class SVM with absolute margin and total sum loss.</span></div>
<div class="line"><a id="l00610" name="l00610"></a><span class="lineno">  610</span><span class="comment"></span><span class="keyword">template</span> &lt;<span class="keyword">class</span> InputT&gt;</div>
<div class="foldopen" id="foldopen00611" data-start="{" data-end="};">
<div class="line"><a id="l00611" name="l00611"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_a_t_s.html">  611</a></span><span class="keyword">class </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear_a_t_s.html" title="Solver for the multi-class SVM with absolute margin and total sum loss.">QpMcLinearATS</a> : <span class="keyword">public</span> <a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;</div>
<div class="line"><a id="l00612" name="l00612"></a><span class="lineno">  612</span>{</div>
<div class="line"><a id="l00613" name="l00613"></a><span class="lineno">  613</span><span class="keyword">public</span>:</div>
<div class="line"><a id="l00614" name="l00614"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_a_t_s.html#aaead2754cb9291e5f6d528cbcb8fe7a4">  614</a></span>    <span class="keyword">typedef</span> <a class="code hl_class" href="classshark_1_1_labeled_data.html" title="Data set for supervised learning.">LabeledData&lt;InputT, unsigned int&gt;</a> <a class="code hl_typedef" href="classshark_1_1_qp_mc_linear_a_t_s.html#aaead2754cb9291e5f6d528cbcb8fe7a4">DatasetType</a>;</div>
<div class="line"><a id="l00615" name="l00615"></a><span class="lineno">  615</span><span class="comment"></span> </div>
<div class="line"><a id="l00616" name="l00616"></a><span class="lineno">  616</span><span class="comment">    /// \brief Constructor</span></div>
<div class="foldopen" id="foldopen00617" data-start="{" data-end="}">
<div class="line"><a id="l00617" name="l00617"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_a_t_s.html#a5a3a765ed2a5d848be8a47d80eec1c98">  617</a></span><span class="comment"></span>    <a class="code hl_function" href="classshark_1_1_qp_mc_linear_a_t_s.html#a5a3a765ed2a5d848be8a47d80eec1c98" title="Constructor.">QpMcLinearATS</a>(</div>
<div class="line"><a id="l00618" name="l00618"></a><span class="lineno">  618</span>            <span class="keyword">const</span> <a class="code hl_class" href="classshark_1_1_labeled_data.html" title="Data set for supervised learning.">DatasetType</a>&amp; dataset,</div>
<div class="line"><a id="l00619" name="l00619"></a><span class="lineno">  619</span>            std::size_t dim,</div>
<div class="line"><a id="l00620" name="l00620"></a><span class="lineno">  620</span>            std::size_t classes)</div>
<div class="line"><a id="l00621" name="l00621"></a><span class="lineno">  621</span>    : <a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;(dataset, dim, classes)</div>
<div class="line"><a id="l00622" name="l00622"></a><span class="lineno">  622</span>    { }</div>
</div>
<div class="line"><a id="l00623" name="l00623"></a><span class="lineno">  623</span> </div>
<div class="line"><a id="l00624" name="l00624"></a><span class="lineno">  624</span><span class="keyword">protected</span>:<span class="comment"></span></div>
<div class="line"><a id="l00625" name="l00625"></a><span class="lineno">  625</span><span class="comment">    /// \brief Compute the gradient from the inner products of the weight vectors with the current sample.</span></div>
<div class="foldopen" id="foldopen00626" data-start="{" data-end="}">
<div class="line"><a id="l00626" name="l00626"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_a_t_s.html#aa878c63a7b0758bc2ad71d77bc65975f">  626</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_a_t_s.html#aa878c63a7b0758bc2ad71d77bc65975f" title="Compute the gradient from the inner products of the weight vectors with the current sample.">calcGradient</a>(RealVector&amp; gradient, RealVector wx, blas::dense_vector_adaptor&lt;double const&gt; <span class="keyword">const</span>&amp; alpha, <span class="keywordtype">double</span> C, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y)</div>
<div class="line"><a id="l00627" name="l00627"></a><span class="lineno">  627</span>    {</div>
<div class="line"><a id="l00628" name="l00628"></a><span class="lineno">  628</span>        <span class="keywordtype">double</span> violation = 0.0;</div>
<div class="line"><a id="l00629" name="l00629"></a><span class="lineno">  629</span>        <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++)</div>
<div class="line"><a id="l00630" name="l00630"></a><span class="lineno">  630</span>        {</div>
<div class="line"><a id="l00631" name="l00631"></a><span class="lineno">  631</span>            <span class="keyword">const</span> <span class="keywordtype">double</span> g = (c == y) ? 1.0 - wx(y) : 1.0 + wx(c);</div>
<div class="line"><a id="l00632" name="l00632"></a><span class="lineno">  632</span>            gradient(c) = g;</div>
<div class="line"><a id="l00633" name="l00633"></a><span class="lineno">  633</span>            <span class="keywordflow">if</span> (g &gt; violation &amp;&amp; alpha(c) &lt; C) violation = g;</div>
<div class="line"><a id="l00634" name="l00634"></a><span class="lineno">  634</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (-g &gt; violation &amp;&amp; alpha(c) &gt; 0.0) violation = -g;</div>
<div class="line"><a id="l00635" name="l00635"></a><span class="lineno">  635</span>        }</div>
<div class="line"><a id="l00636" name="l00636"></a><span class="lineno">  636</span>        <span class="keywordflow">return</span> violation;</div>
<div class="line"><a id="l00637" name="l00637"></a><span class="lineno">  637</span>    }</div>
</div>
<div class="line"><a id="l00638" name="l00638"></a><span class="lineno">  638</span><span class="comment"></span> </div>
<div class="line"><a id="l00639" name="l00639"></a><span class="lineno">  639</span><span class="comment">    /// \brief Update the weight vectors (primal variables) after a step on the dual variables.</span></div>
<div class="foldopen" id="foldopen00640" data-start="{" data-end="}">
<div class="line"><a id="l00640" name="l00640"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_a_t_s.html#a879e147e3dd09399635bfc2df2f46013">  640</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_a_t_s.html#a879e147e3dd09399635bfc2df2f46013" title="Update the weight vectors (primal variables) after a step on the dual variables.">updateWeightVectors</a>(RealMatrix&amp; w, RealVector <span class="keyword">const</span>&amp; mu, std::size_t index)</div>
<div class="line"><a id="l00641" name="l00641"></a><span class="lineno">  641</span>    {</div>
<div class="line"><a id="l00642" name="l00642"></a><span class="lineno">  642</span>        <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y = <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">m_data</a>[index].label;</div>
<div class="line"><a id="l00643" name="l00643"></a><span class="lineno">  643</span>        <span class="keywordtype">double</span> <a class="code hl_function" href="namespaceshark.html#a6ae694efca57e84792fcff090223437e" title="Calculates the mean vector of the input vectors.">mean</a> = -2.0 * mu(y);</div>
<div class="line"><a id="l00644" name="l00644"></a><span class="lineno">  644</span>        <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) <a class="code hl_function" href="namespaceshark.html#a6ae694efca57e84792fcff090223437e" title="Calculates the mean vector of the input vectors.">mean</a> += mu(c);</div>
<div class="line"><a id="l00645" name="l00645"></a><span class="lineno">  645</span>        <a class="code hl_function" href="namespaceshark.html#a6ae694efca57e84792fcff090223437e" title="Calculates the mean vector of the input vectors.">mean</a> /= (double)<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l00646" name="l00646"></a><span class="lineno">  646</span>        RealVector step(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>);</div>
<div class="line"><a id="l00647" name="l00647"></a><span class="lineno">  647</span>        <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) step(c) = ((c == y) ? (mu(c) + <a class="code hl_function" href="namespaceshark.html#a6ae694efca57e84792fcff090223437e" title="Calculates the mean vector of the input vectors.">mean</a>) : (<a class="code hl_function" href="namespaceshark.html#a6ae694efca57e84792fcff090223437e" title="Calculates the mean vector of the input vectors.">mean</a> - mu(c)));</div>
<div class="line"><a id="l00648" name="l00648"></a><span class="lineno">  648</span>        <a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#a64edc8279169777bf9ef05052a412acd">add_scaled</a>(w, step, <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">m_data</a>[index].input);</div>
<div class="line"><a id="l00649" name="l00649"></a><span class="lineno">  649</span>    }</div>
</div>
<div class="line"><a id="l00650" name="l00650"></a><span class="lineno">  650</span><span class="comment"></span> </div>
<div class="line"><a id="l00651" name="l00651"></a><span class="lineno">  651</span><span class="comment">    /// \brief Solve the sub-problem posed by a single training example.</span></div>
<div class="foldopen" id="foldopen00652" data-start="{" data-end="}">
<div class="line"><a id="l00652" name="l00652"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_a_t_s.html#ab28cf05fe5056dee19e00821473f62b6">  652</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_a_t_s.html#ab28cf05fe5056dee19e00821473f62b6" title="Solve the sub-problem posed by a single training example.">solveSub</a>(<span class="keywordtype">double</span> epsilon, RealVector&amp; gradient, <span class="keywordtype">double</span> q, <span class="keywordtype">double</span> C, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y, blas::dense_vector_adaptor&lt;double&gt;&amp; alpha, RealVector&amp; mu)</div>
<div class="line"><a id="l00653" name="l00653"></a><span class="lineno">  653</span>    {</div>
<div class="line"><a id="l00654" name="l00654"></a><span class="lineno">  654</span>        <span class="keyword">const</span> <span class="keywordtype">double</span> ood = 1.0 / <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l00655" name="l00655"></a><span class="lineno">  655</span>        <span class="keyword">const</span> <span class="keywordtype">double</span> qq = (1.0 - ood) * q;</div>
<div class="line"><a id="l00656" name="l00656"></a><span class="lineno">  656</span>        <span class="keywordtype">double</span> gain = 0.0;</div>
<div class="line"><a id="l00657" name="l00657"></a><span class="lineno">  657</span> </div>
<div class="line"><a id="l00658" name="l00658"></a><span class="lineno">  658</span>        <span class="comment">// SMO loop</span></div>
<div class="line"><a id="l00659" name="l00659"></a><span class="lineno">  659</span>        <span class="keywordtype">size_t</span> iter, maxiter = 10 * <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l00660" name="l00660"></a><span class="lineno">  660</span>        <span class="keywordflow">for</span> (iter=0; iter&lt;maxiter; iter++)</div>
<div class="line"><a id="l00661" name="l00661"></a><span class="lineno">  661</span>        {</div>
<div class="line"><a id="l00662" name="l00662"></a><span class="lineno">  662</span>            <span class="comment">// select working set</span></div>
<div class="line"><a id="l00663" name="l00663"></a><span class="lineno">  663</span>            std::size_t idx = 0;</div>
<div class="line"><a id="l00664" name="l00664"></a><span class="lineno">  664</span>            <span class="keywordtype">double</span> kkt = 0.0;</div>
<div class="line"><a id="l00665" name="l00665"></a><span class="lineno">  665</span>            <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++)</div>
<div class="line"><a id="l00666" name="l00666"></a><span class="lineno">  666</span>            {</div>
<div class="line"><a id="l00667" name="l00667"></a><span class="lineno">  667</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> g = gradient(c);</div>
<div class="line"><a id="l00668" name="l00668"></a><span class="lineno">  668</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> a = alpha(c);</div>
<div class="line"><a id="l00669" name="l00669"></a><span class="lineno">  669</span>                <span class="keywordflow">if</span> (g &gt; kkt &amp;&amp; a &lt; C) { kkt = g; idx = c; }</div>
<div class="line"><a id="l00670" name="l00670"></a><span class="lineno">  670</span>                <span class="keywordflow">else</span> <span class="keywordflow">if</span> (-g &gt; kkt &amp;&amp; a &gt; 0.0) { kkt = -g; idx = c; }</div>
<div class="line"><a id="l00671" name="l00671"></a><span class="lineno">  671</span>            }</div>
<div class="line"><a id="l00672" name="l00672"></a><span class="lineno">  672</span> </div>
<div class="line"><a id="l00673" name="l00673"></a><span class="lineno">  673</span>            <span class="comment">// check stopping criterion</span></div>
<div class="line"><a id="l00674" name="l00674"></a><span class="lineno">  674</span>            <span class="keywordflow">if</span> (kkt &lt; epsilon) <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00675" name="l00675"></a><span class="lineno">  675</span> </div>
<div class="line"><a id="l00676" name="l00676"></a><span class="lineno">  676</span>            <span class="comment">// perform step</span></div>
<div class="line"><a id="l00677" name="l00677"></a><span class="lineno">  677</span>            <span class="keyword">const</span> <span class="keywordtype">double</span> a = alpha(idx);</div>
<div class="line"><a id="l00678" name="l00678"></a><span class="lineno">  678</span>            <span class="keyword">const</span> <span class="keywordtype">double</span> g = gradient(idx);</div>
<div class="line"><a id="l00679" name="l00679"></a><span class="lineno">  679</span>            <span class="keywordtype">double</span> m = g / qq;</div>
<div class="line"><a id="l00680" name="l00680"></a><span class="lineno">  680</span>            <span class="keywordtype">double</span> a_new = a + m;</div>
<div class="line"><a id="l00681" name="l00681"></a><span class="lineno">  681</span>            <span class="keywordflow">if</span> (a_new &lt;= 0.0)</div>
<div class="line"><a id="l00682" name="l00682"></a><span class="lineno">  682</span>            {</div>
<div class="line"><a id="l00683" name="l00683"></a><span class="lineno">  683</span>                m = -a;</div>
<div class="line"><a id="l00684" name="l00684"></a><span class="lineno">  684</span>                a_new = 0.0;</div>
<div class="line"><a id="l00685" name="l00685"></a><span class="lineno">  685</span>            }</div>
<div class="line"><a id="l00686" name="l00686"></a><span class="lineno">  686</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (a_new &gt;= C)</div>
<div class="line"><a id="l00687" name="l00687"></a><span class="lineno">  687</span>            {</div>
<div class="line"><a id="l00688" name="l00688"></a><span class="lineno">  688</span>                m = C - a;</div>
<div class="line"><a id="l00689" name="l00689"></a><span class="lineno">  689</span>                a_new = C;</div>
<div class="line"><a id="l00690" name="l00690"></a><span class="lineno">  690</span>            }</div>
<div class="line"><a id="l00691" name="l00691"></a><span class="lineno">  691</span>            alpha(idx) = a_new;</div>
<div class="line"><a id="l00692" name="l00692"></a><span class="lineno">  692</span>            mu(idx) += m;</div>
<div class="line"><a id="l00693" name="l00693"></a><span class="lineno">  693</span> </div>
<div class="line"><a id="l00694" name="l00694"></a><span class="lineno">  694</span>            <span class="comment">// update gradient and total gain</span></div>
<div class="line"><a id="l00695" name="l00695"></a><span class="lineno">  695</span>            <span class="keyword">const</span> <span class="keywordtype">double</span> dg = m * q;</div>
<div class="line"><a id="l00696" name="l00696"></a><span class="lineno">  696</span>            <span class="keyword">const</span> <span class="keywordtype">double</span> dgc = dg / <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l00697" name="l00697"></a><span class="lineno">  697</span>            <span class="keywordflow">if</span> (idx == y)</div>
<div class="line"><a id="l00698" name="l00698"></a><span class="lineno">  698</span>            {</div>
<div class="line"><a id="l00699" name="l00699"></a><span class="lineno">  699</span>                <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) gradient(c) -= dgc;</div>
<div class="line"><a id="l00700" name="l00700"></a><span class="lineno">  700</span>                gradient(idx) -= dg - 2.0 * dgc;</div>
<div class="line"><a id="l00701" name="l00701"></a><span class="lineno">  701</span>            }</div>
<div class="line"><a id="l00702" name="l00702"></a><span class="lineno">  702</span>            <span class="keywordflow">else</span></div>
<div class="line"><a id="l00703" name="l00703"></a><span class="lineno">  703</span>            {</div>
<div class="line"><a id="l00704" name="l00704"></a><span class="lineno">  704</span>                <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) gradient(c) += (c == y) ? -dgc : dgc;</div>
<div class="line"><a id="l00705" name="l00705"></a><span class="lineno">  705</span>                gradient(idx) -= dg;</div>
<div class="line"><a id="l00706" name="l00706"></a><span class="lineno">  706</span>            }</div>
<div class="line"><a id="l00707" name="l00707"></a><span class="lineno">  707</span> </div>
<div class="line"><a id="l00708" name="l00708"></a><span class="lineno">  708</span>            gain += m * (g - 0.5 * (dg - dgc));</div>
<div class="line"><a id="l00709" name="l00709"></a><span class="lineno">  709</span>        }</div>
<div class="line"><a id="l00710" name="l00710"></a><span class="lineno">  710</span> </div>
<div class="line"><a id="l00711" name="l00711"></a><span class="lineno">  711</span>        <span class="keywordflow">return</span> gain;</div>
<div class="line"><a id="l00712" name="l00712"></a><span class="lineno">  712</span>    }</div>
</div>
<div class="line"><a id="l00713" name="l00713"></a><span class="lineno">  713</span> </div>
<div class="line"><a id="l00714" name="l00714"></a><span class="lineno">  714</span><span class="keyword">protected</span>:</div>
<div class="line"><a id="l00715" name="l00715"></a><span class="lineno">  715</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#a64edc8279169777bf9ef05052a412acd">::add_scaled</a>;</div>
<div class="line"><a id="l00716" name="l00716"></a><span class="lineno">  716</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">::m_data</a>;</div>
<div class="line"><a id="l00717" name="l00717"></a><span class="lineno">  717</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">::m_classes</a>;</div>
<div class="line"><a id="l00718" name="l00718"></a><span class="lineno">  718</span>};</div>
</div>
<div class="line"><a id="l00719" name="l00719"></a><span class="lineno">  719</span> </div>
<div class="line"><a id="l00720" name="l00720"></a><span class="lineno">  720</span><span class="comment"></span> </div>
<div class="line"><a id="l00721" name="l00721"></a><span class="lineno">  721</span><span class="comment">/// \brief Solver for the multi-class maximum margin regression SVM</span></div>
<div class="line"><a id="l00722" name="l00722"></a><span class="lineno">  722</span><span class="comment"></span><span class="keyword">template</span> &lt;<span class="keyword">class</span> InputT&gt;</div>
<div class="foldopen" id="foldopen00723" data-start="{" data-end="};">
<div class="line"><a id="l00723" name="l00723"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_m_m_r.html">  723</a></span><span class="keyword">class </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear_m_m_r.html" title="Solver for the multi-class maximum margin regression SVM.">QpMcLinearMMR</a> : <span class="keyword">public</span> <a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;</div>
<div class="line"><a id="l00724" name="l00724"></a><span class="lineno">  724</span>{</div>
<div class="line"><a id="l00725" name="l00725"></a><span class="lineno">  725</span><span class="keyword">public</span>:</div>
<div class="line"><a id="l00726" name="l00726"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_m_m_r.html#a601bad9efffcbb3f7e95a7dd634e62c7">  726</a></span>    <span class="keyword">typedef</span> <a class="code hl_class" href="classshark_1_1_labeled_data.html" title="Data set for supervised learning.">LabeledData&lt;InputT, unsigned int&gt;</a> <a class="code hl_typedef" href="classshark_1_1_qp_mc_linear_m_m_r.html#a601bad9efffcbb3f7e95a7dd634e62c7">DatasetType</a>;</div>
<div class="line"><a id="l00727" name="l00727"></a><span class="lineno">  727</span><span class="comment"></span> </div>
<div class="line"><a id="l00728" name="l00728"></a><span class="lineno">  728</span><span class="comment">    /// \brief Constructor</span></div>
<div class="foldopen" id="foldopen00729" data-start="{" data-end="}">
<div class="line"><a id="l00729" name="l00729"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_m_m_r.html#a5af936784fc41fa371c1a47fe1ffd548">  729</a></span><span class="comment"></span>    <a class="code hl_function" href="classshark_1_1_qp_mc_linear_m_m_r.html#a5af936784fc41fa371c1a47fe1ffd548" title="Constructor.">QpMcLinearMMR</a>(</div>
<div class="line"><a id="l00730" name="l00730"></a><span class="lineno">  730</span>            <span class="keyword">const</span> <a class="code hl_class" href="classshark_1_1_labeled_data.html" title="Data set for supervised learning.">DatasetType</a>&amp; dataset,</div>
<div class="line"><a id="l00731" name="l00731"></a><span class="lineno">  731</span>            std::size_t dim,</div>
<div class="line"><a id="l00732" name="l00732"></a><span class="lineno">  732</span>            std::size_t classes)</div>
<div class="line"><a id="l00733" name="l00733"></a><span class="lineno">  733</span>    : <a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;(dataset, dim, classes)</div>
<div class="line"><a id="l00734" name="l00734"></a><span class="lineno">  734</span>    { }</div>
</div>
<div class="line"><a id="l00735" name="l00735"></a><span class="lineno">  735</span> </div>
<div class="line"><a id="l00736" name="l00736"></a><span class="lineno">  736</span><span class="keyword">protected</span>:<span class="comment"></span></div>
<div class="line"><a id="l00737" name="l00737"></a><span class="lineno">  737</span><span class="comment">    /// \brief Compute the gradient from the inner products of the weight vectors with the current sample.</span></div>
<div class="foldopen" id="foldopen00738" data-start="{" data-end="}">
<div class="line"><a id="l00738" name="l00738"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_m_m_r.html#a63cf5cf3a2059c597bc266cc4cd35674">  738</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_m_m_r.html#a63cf5cf3a2059c597bc266cc4cd35674" title="Compute the gradient from the inner products of the weight vectors with the current sample.">calcGradient</a>(RealVector&amp; gradient, RealVector wx, blas::dense_vector_adaptor&lt;double const&gt; <span class="keyword">const</span>&amp; alpha, <span class="keywordtype">double</span> C, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y)</div>
<div class="line"><a id="l00739" name="l00739"></a><span class="lineno">  739</span>    {</div>
<div class="line"><a id="l00740" name="l00740"></a><span class="lineno">  740</span>        <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) gradient(c) = 0.0;</div>
<div class="line"><a id="l00741" name="l00741"></a><span class="lineno">  741</span>        <span class="keyword">const</span> <span class="keywordtype">double</span> g = 1.0 - wx(y);</div>
<div class="line"><a id="l00742" name="l00742"></a><span class="lineno">  742</span>        gradient(y) = g;</div>
<div class="line"><a id="l00743" name="l00743"></a><span class="lineno">  743</span>        <span class="keyword">const</span> <span class="keywordtype">double</span> a = alpha(0);</div>
<div class="line"><a id="l00744" name="l00744"></a><span class="lineno">  744</span>        <span class="keywordflow">if</span> (g &gt; 0.0)</div>
<div class="line"><a id="l00745" name="l00745"></a><span class="lineno">  745</span>        {</div>
<div class="line"><a id="l00746" name="l00746"></a><span class="lineno">  746</span>            <span class="keywordflow">if</span> (a == C) <span class="keywordflow">return</span> 0.0;</div>
<div class="line"><a id="l00747" name="l00747"></a><span class="lineno">  747</span>            <span class="keywordflow">else</span> <span class="keywordflow">return</span> g;</div>
<div class="line"><a id="l00748" name="l00748"></a><span class="lineno">  748</span>        }</div>
<div class="line"><a id="l00749" name="l00749"></a><span class="lineno">  749</span>        <span class="keywordflow">else</span></div>
<div class="line"><a id="l00750" name="l00750"></a><span class="lineno">  750</span>        {</div>
<div class="line"><a id="l00751" name="l00751"></a><span class="lineno">  751</span>            <span class="keywordflow">if</span> (a == 0.0) <span class="keywordflow">return</span> 0.0;</div>
<div class="line"><a id="l00752" name="l00752"></a><span class="lineno">  752</span>            <span class="keywordflow">else</span> <span class="keywordflow">return</span> -g;</div>
<div class="line"><a id="l00753" name="l00753"></a><span class="lineno">  753</span>        }</div>
<div class="line"><a id="l00754" name="l00754"></a><span class="lineno">  754</span>    }</div>
</div>
<div class="line"><a id="l00755" name="l00755"></a><span class="lineno">  755</span><span class="comment"></span> </div>
<div class="line"><a id="l00756" name="l00756"></a><span class="lineno">  756</span><span class="comment">    /// \brief Update the weight vectors (primal variables) after a step on the dual variables.</span></div>
<div class="foldopen" id="foldopen00757" data-start="{" data-end="}">
<div class="line"><a id="l00757" name="l00757"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_m_m_r.html#a93f9f804635fb731f339bf8419776efd">  757</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_m_m_r.html#a93f9f804635fb731f339bf8419776efd" title="Update the weight vectors (primal variables) after a step on the dual variables.">updateWeightVectors</a>(RealMatrix&amp; w, RealVector <span class="keyword">const</span>&amp; mu, std::size_t index)</div>
<div class="line"><a id="l00758" name="l00758"></a><span class="lineno">  758</span>    {</div>
<div class="line"><a id="l00759" name="l00759"></a><span class="lineno">  759</span>        <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y = <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">m_data</a>[index].label;</div>
<div class="line"><a id="l00760" name="l00760"></a><span class="lineno">  760</span>        <span class="keywordtype">double</span> s = mu(0);</div>
<div class="line"><a id="l00761" name="l00761"></a><span class="lineno">  761</span>        <span class="keywordtype">double</span> sc = -s / <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l00762" name="l00762"></a><span class="lineno">  762</span>        <span class="keywordtype">double</span> sy = s + sc;</div>
<div class="line"><a id="l00763" name="l00763"></a><span class="lineno">  763</span>        RealVector step(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>);</div>
<div class="line"><a id="l00764" name="l00764"></a><span class="lineno">  764</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) step(c) = (c == y) ? sy : sc;</div>
<div class="line"><a id="l00765" name="l00765"></a><span class="lineno">  765</span>        <a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#a64edc8279169777bf9ef05052a412acd">add_scaled</a>(w, step, <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">m_data</a>[index].input);</div>
<div class="line"><a id="l00766" name="l00766"></a><span class="lineno">  766</span>    }</div>
</div>
<div class="line"><a id="l00767" name="l00767"></a><span class="lineno">  767</span><span class="comment"></span> </div>
<div class="line"><a id="l00768" name="l00768"></a><span class="lineno">  768</span><span class="comment">    /// \brief Solve the sub-problem posed by a single training example.</span></div>
<div class="foldopen" id="foldopen00769" data-start="{" data-end="}">
<div class="line"><a id="l00769" name="l00769"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_m_m_r.html#a08dec16354913fbbad8e3628b608c4e1">  769</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_m_m_r.html#a08dec16354913fbbad8e3628b608c4e1" title="Solve the sub-problem posed by a single training example.">solveSub</a>(<span class="keywordtype">double</span> epsilon, RealVector&amp; gradient, <span class="keywordtype">double</span> q, <span class="keywordtype">double</span> C, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y, blas::dense_vector_adaptor&lt;double&gt;&amp; alpha, RealVector&amp; mu)</div>
<div class="line"><a id="l00770" name="l00770"></a><span class="lineno">  770</span>    {</div>
<div class="line"><a id="l00771" name="l00771"></a><span class="lineno">  771</span>        <span class="keyword">const</span> <span class="keywordtype">double</span> ood = 1.0 / <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l00772" name="l00772"></a><span class="lineno">  772</span>        <span class="keyword">const</span> <span class="keywordtype">double</span> qq = (1.0 - ood) * q;</div>
<div class="line"><a id="l00773" name="l00773"></a><span class="lineno">  773</span> </div>
<div class="line"><a id="l00774" name="l00774"></a><span class="lineno">  774</span>        <span class="keywordtype">double</span> kkt = 0.0;</div>
<div class="line"><a id="l00775" name="l00775"></a><span class="lineno">  775</span>        <span class="keyword">const</span> <span class="keywordtype">double</span> g = gradient(y);</div>
<div class="line"><a id="l00776" name="l00776"></a><span class="lineno">  776</span>        <span class="keyword">const</span> <span class="keywordtype">double</span> a = alpha(0);</div>
<div class="line"><a id="l00777" name="l00777"></a><span class="lineno">  777</span>        <span class="keywordflow">if</span> (g &gt; kkt &amp;&amp; a &lt; C) kkt = g;</div>
<div class="line"><a id="l00778" name="l00778"></a><span class="lineno">  778</span>        <span class="keywordflow">else</span> <span class="keywordflow">if</span> (-g &gt; kkt &amp;&amp; a &gt; 0.0) kkt = -g;</div>
<div class="line"><a id="l00779" name="l00779"></a><span class="lineno">  779</span> </div>
<div class="line"><a id="l00780" name="l00780"></a><span class="lineno">  780</span>        <span class="comment">// check stopping criterion</span></div>
<div class="line"><a id="l00781" name="l00781"></a><span class="lineno">  781</span>        <span class="keywordflow">if</span> (kkt &lt; epsilon) <span class="keywordflow">return</span> 0.0;</div>
<div class="line"><a id="l00782" name="l00782"></a><span class="lineno">  782</span> </div>
<div class="line"><a id="l00783" name="l00783"></a><span class="lineno">  783</span>        <span class="comment">// perform step</span></div>
<div class="line"><a id="l00784" name="l00784"></a><span class="lineno">  784</span>        <span class="keywordtype">double</span> m = g / qq;</div>
<div class="line"><a id="l00785" name="l00785"></a><span class="lineno">  785</span>        <span class="keywordtype">double</span> a_new = a + m;</div>
<div class="line"><a id="l00786" name="l00786"></a><span class="lineno">  786</span>        <span class="keywordflow">if</span> (a_new &lt;= 0.0)</div>
<div class="line"><a id="l00787" name="l00787"></a><span class="lineno">  787</span>        {</div>
<div class="line"><a id="l00788" name="l00788"></a><span class="lineno">  788</span>            m = -a;</div>
<div class="line"><a id="l00789" name="l00789"></a><span class="lineno">  789</span>            a_new = 0.0;</div>
<div class="line"><a id="l00790" name="l00790"></a><span class="lineno">  790</span>        }</div>
<div class="line"><a id="l00791" name="l00791"></a><span class="lineno">  791</span>        <span class="keywordflow">else</span> <span class="keywordflow">if</span> (a_new &gt;= C)</div>
<div class="line"><a id="l00792" name="l00792"></a><span class="lineno">  792</span>        {</div>
<div class="line"><a id="l00793" name="l00793"></a><span class="lineno">  793</span>            m = C - a;</div>
<div class="line"><a id="l00794" name="l00794"></a><span class="lineno">  794</span>            a_new = C;</div>
<div class="line"><a id="l00795" name="l00795"></a><span class="lineno">  795</span>        }</div>
<div class="line"><a id="l00796" name="l00796"></a><span class="lineno">  796</span>        alpha(0) = a_new;</div>
<div class="line"><a id="l00797" name="l00797"></a><span class="lineno">  797</span>        mu(0) = m;</div>
<div class="line"><a id="l00798" name="l00798"></a><span class="lineno">  798</span> </div>
<div class="line"><a id="l00799" name="l00799"></a><span class="lineno">  799</span>        <span class="comment">// return the gain</span></div>
<div class="line"><a id="l00800" name="l00800"></a><span class="lineno">  800</span>        <span class="keywordflow">return</span> m * (g - 0.5 * m * qq);</div>
<div class="line"><a id="l00801" name="l00801"></a><span class="lineno">  801</span>    }</div>
</div>
<div class="line"><a id="l00802" name="l00802"></a><span class="lineno">  802</span> </div>
<div class="line"><a id="l00803" name="l00803"></a><span class="lineno">  803</span><span class="keyword">protected</span>:</div>
<div class="line"><a id="l00804" name="l00804"></a><span class="lineno">  804</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#a64edc8279169777bf9ef05052a412acd">::add_scaled</a>;</div>
<div class="line"><a id="l00805" name="l00805"></a><span class="lineno">  805</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">::m_data</a>;</div>
<div class="line"><a id="l00806" name="l00806"></a><span class="lineno">  806</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">::m_classes</a>;</div>
<div class="line"><a id="l00807" name="l00807"></a><span class="lineno">  807</span>};</div>
</div>
<div class="line"><a id="l00808" name="l00808"></a><span class="lineno">  808</span> </div>
<div class="line"><a id="l00809" name="l00809"></a><span class="lineno">  809</span><span class="comment"></span> </div>
<div class="line"><a id="l00810" name="l00810"></a><span class="lineno">  810</span><span class="comment">/// \brief Solver for the multi-class SVM by Crammer &amp; Singer.</span></div>
<div class="line"><a id="l00811" name="l00811"></a><span class="lineno">  811</span><span class="comment"></span><span class="keyword">template</span> &lt;<span class="keyword">class</span> InputT&gt;</div>
<div class="foldopen" id="foldopen00812" data-start="{" data-end="};">
<div class="line"><a id="l00812" name="l00812"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_c_s.html">  812</a></span><span class="keyword">class </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear_c_s.html" title="Solver for the multi-class SVM by Crammer &amp; Singer.">QpMcLinearCS</a> : <span class="keyword">public</span> <a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;</div>
<div class="line"><a id="l00813" name="l00813"></a><span class="lineno">  813</span>{</div>
<div class="line"><a id="l00814" name="l00814"></a><span class="lineno">  814</span><span class="keyword">public</span>:</div>
<div class="line"><a id="l00815" name="l00815"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_c_s.html#a59105bb31b6de78f13982629b32eb178">  815</a></span>    <span class="keyword">typedef</span> <a class="code hl_class" href="classshark_1_1_labeled_data.html" title="Data set for supervised learning.">LabeledData&lt;InputT, unsigned int&gt;</a> <a class="code hl_typedef" href="classshark_1_1_qp_mc_linear_c_s.html#a59105bb31b6de78f13982629b32eb178">DatasetType</a>;</div>
<div class="line"><a id="l00816" name="l00816"></a><span class="lineno">  816</span><span class="comment"></span> </div>
<div class="line"><a id="l00817" name="l00817"></a><span class="lineno">  817</span><span class="comment">    /// \brief Constructor</span></div>
<div class="foldopen" id="foldopen00818" data-start="{" data-end="}">
<div class="line"><a id="l00818" name="l00818"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_c_s.html#a1040b9d355cee9ce6ada95fd73df6667">  818</a></span><span class="comment"></span>    <a class="code hl_function" href="classshark_1_1_qp_mc_linear_c_s.html#a1040b9d355cee9ce6ada95fd73df6667" title="Constructor.">QpMcLinearCS</a>(</div>
<div class="line"><a id="l00819" name="l00819"></a><span class="lineno">  819</span>            <span class="keyword">const</span> <a class="code hl_class" href="classshark_1_1_labeled_data.html" title="Data set for supervised learning.">DatasetType</a>&amp; dataset,</div>
<div class="line"><a id="l00820" name="l00820"></a><span class="lineno">  820</span>            std::size_t dim,</div>
<div class="line"><a id="l00821" name="l00821"></a><span class="lineno">  821</span>            std::size_t classes)</div>
<div class="line"><a id="l00822" name="l00822"></a><span class="lineno">  822</span>    : <a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;(dataset, dim, classes)</div>
<div class="line"><a id="l00823" name="l00823"></a><span class="lineno">  823</span>    { }</div>
</div>
<div class="line"><a id="l00824" name="l00824"></a><span class="lineno">  824</span> </div>
<div class="line"><a id="l00825" name="l00825"></a><span class="lineno">  825</span><span class="keyword">protected</span>:<span class="comment"></span></div>
<div class="line"><a id="l00826" name="l00826"></a><span class="lineno">  826</span><span class="comment">    /// \brief Compute the gradient from the inner products of the weight vectors with the current sample.</span></div>
<div class="foldopen" id="foldopen00827" data-start="{" data-end="}">
<div class="line"><a id="l00827" name="l00827"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_c_s.html#a800c787ffc88f44571a67e66f83d9f2b">  827</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_c_s.html#a800c787ffc88f44571a67e66f83d9f2b" title="Compute the gradient from the inner products of the weight vectors with the current sample.">calcGradient</a>(RealVector&amp; gradient, RealVector wx, blas::dense_vector_adaptor&lt;double const&gt; <span class="keyword">const</span>&amp; alpha, <span class="keywordtype">double</span> C, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y)</div>
<div class="line"><a id="l00828" name="l00828"></a><span class="lineno">  828</span>    {</div>
<div class="line"><a id="l00829" name="l00829"></a><span class="lineno">  829</span>        <span class="keywordflow">if</span> (alpha(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>) &lt; C)</div>
<div class="line"><a id="l00830" name="l00830"></a><span class="lineno">  830</span>        {</div>
<div class="line"><a id="l00831" name="l00831"></a><span class="lineno">  831</span>            <span class="keywordtype">double</span> violation = 0.0;</div>
<div class="line"><a id="l00832" name="l00832"></a><span class="lineno">  832</span>            <span class="keywordflow">for</span> (std::size_t c=0; c&lt;wx.size(); c++)</div>
<div class="line"><a id="l00833" name="l00833"></a><span class="lineno">  833</span>            {</div>
<div class="line"><a id="l00834" name="l00834"></a><span class="lineno">  834</span>                <span class="keywordflow">if</span> (c == y)</div>
<div class="line"><a id="l00835" name="l00835"></a><span class="lineno">  835</span>                {</div>
<div class="line"><a id="l00836" name="l00836"></a><span class="lineno">  836</span>                    gradient(c) = 0.0;</div>
<div class="line"><a id="l00837" name="l00837"></a><span class="lineno">  837</span>                }</div>
<div class="line"><a id="l00838" name="l00838"></a><span class="lineno">  838</span>                <span class="keywordflow">else</span></div>
<div class="line"><a id="l00839" name="l00839"></a><span class="lineno">  839</span>                {</div>
<div class="line"><a id="l00840" name="l00840"></a><span class="lineno">  840</span>                    <span class="keyword">const</span> <span class="keywordtype">double</span> g = 1.0 - 0.5 * (wx(y) - wx(c));</div>
<div class="line"><a id="l00841" name="l00841"></a><span class="lineno">  841</span>                    gradient(c) = g;</div>
<div class="line"><a id="l00842" name="l00842"></a><span class="lineno">  842</span>                    <span class="keywordflow">if</span> (g &gt; violation) violation = g;</div>
<div class="line"><a id="l00843" name="l00843"></a><span class="lineno">  843</span>                    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (-g &gt; violation &amp;&amp; alpha(c) &gt; 0.0) violation = -g;</div>
<div class="line"><a id="l00844" name="l00844"></a><span class="lineno">  844</span>                }</div>
<div class="line"><a id="l00845" name="l00845"></a><span class="lineno">  845</span>            }</div>
<div class="line"><a id="l00846" name="l00846"></a><span class="lineno">  846</span>            <span class="keywordflow">return</span> violation;</div>
<div class="line"><a id="l00847" name="l00847"></a><span class="lineno">  847</span>        }</div>
<div class="line"><a id="l00848" name="l00848"></a><span class="lineno">  848</span>        <span class="keywordflow">else</span></div>
<div class="line"><a id="l00849" name="l00849"></a><span class="lineno">  849</span>        {</div>
<div class="line"><a id="l00850" name="l00850"></a><span class="lineno">  850</span>            <span class="comment">// double kkt_up = -1e100, kkt_down = 1e100;</span></div>
<div class="line"><a id="l00851" name="l00851"></a><span class="lineno">  851</span>            <span class="keywordtype">double</span> kkt_up = 0.0, kkt_down = 1e100;</div>
<div class="line"><a id="l00852" name="l00852"></a><span class="lineno">  852</span>            <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++)</div>
<div class="line"><a id="l00853" name="l00853"></a><span class="lineno">  853</span>            {</div>
<div class="line"><a id="l00854" name="l00854"></a><span class="lineno">  854</span>                <span class="keywordflow">if</span> (c == y)</div>
<div class="line"><a id="l00855" name="l00855"></a><span class="lineno">  855</span>                {</div>
<div class="line"><a id="l00856" name="l00856"></a><span class="lineno">  856</span>                    gradient(c) = 0.0;</div>
<div class="line"><a id="l00857" name="l00857"></a><span class="lineno">  857</span>                }</div>
<div class="line"><a id="l00858" name="l00858"></a><span class="lineno">  858</span>                <span class="keywordflow">else</span></div>
<div class="line"><a id="l00859" name="l00859"></a><span class="lineno">  859</span>                {</div>
<div class="line"><a id="l00860" name="l00860"></a><span class="lineno">  860</span>                    <span class="keyword">const</span> <span class="keywordtype">double</span> g = 1.0 - 0.5 * (wx(y) - wx(c));</div>
<div class="line"><a id="l00861" name="l00861"></a><span class="lineno">  861</span>                    gradient(c) = g;</div>
<div class="line"><a id="l00862" name="l00862"></a><span class="lineno">  862</span>                    <span class="keywordflow">if</span> (g &gt; kkt_up &amp;&amp; alpha(c) &lt; C) kkt_up = g;</div>
<div class="line"><a id="l00863" name="l00863"></a><span class="lineno">  863</span>                    <span class="keywordflow">if</span> (g &lt; kkt_down &amp;&amp; alpha(c) &gt; 0.0) kkt_down = g;</div>
<div class="line"><a id="l00864" name="l00864"></a><span class="lineno">  864</span>                }</div>
<div class="line"><a id="l00865" name="l00865"></a><span class="lineno">  865</span>            }</div>
<div class="line"><a id="l00866" name="l00866"></a><span class="lineno">  866</span>            <span class="keywordflow">return</span> std::max(0.0, kkt_up - kkt_down);</div>
<div class="line"><a id="l00867" name="l00867"></a><span class="lineno">  867</span>        }</div>
<div class="line"><a id="l00868" name="l00868"></a><span class="lineno">  868</span>    }</div>
</div>
<div class="line"><a id="l00869" name="l00869"></a><span class="lineno">  869</span><span class="comment"></span> </div>
<div class="line"><a id="l00870" name="l00870"></a><span class="lineno">  870</span><span class="comment">    /// \brief Update the weight vectors (primal variables) after a step on the dual variables.</span></div>
<div class="foldopen" id="foldopen00871" data-start="{" data-end="}">
<div class="line"><a id="l00871" name="l00871"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_c_s.html#a55c0490023e02754a2cdfad01bfa05ce">  871</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_c_s.html#a55c0490023e02754a2cdfad01bfa05ce" title="Update the weight vectors (primal variables) after a step on the dual variables.">updateWeightVectors</a>(RealMatrix&amp; w, RealVector <span class="keyword">const</span>&amp; mu, std::size_t index)</div>
<div class="line"><a id="l00872" name="l00872"></a><span class="lineno">  872</span>    {</div>
<div class="line"><a id="l00873" name="l00873"></a><span class="lineno">  873</span>        <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y = <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">m_data</a>[index].label;</div>
<div class="line"><a id="l00874" name="l00874"></a><span class="lineno">  874</span>        <span class="keywordtype">double</span> sum_mu = 0.0;</div>
<div class="line"><a id="l00875" name="l00875"></a><span class="lineno">  875</span>        <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) <span class="keywordflow">if</span> (c != y) sum_mu += mu(c);</div>
<div class="line"><a id="l00876" name="l00876"></a><span class="lineno">  876</span>        RealVector step(-0.5 * mu);</div>
<div class="line"><a id="l00877" name="l00877"></a><span class="lineno">  877</span>        step(y) = 0.5 * sum_mu;</div>
<div class="line"><a id="l00878" name="l00878"></a><span class="lineno">  878</span>        <a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#a64edc8279169777bf9ef05052a412acd">add_scaled</a>(w, step, <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">m_data</a>[index].input);</div>
<div class="line"><a id="l00879" name="l00879"></a><span class="lineno">  879</span>    }</div>
</div>
<div class="line"><a id="l00880" name="l00880"></a><span class="lineno">  880</span><span class="comment"></span> </div>
<div class="line"><a id="l00881" name="l00881"></a><span class="lineno">  881</span><span class="comment">    /// \brief Solve the sub-problem posed by a single training example.</span></div>
<div class="foldopen" id="foldopen00882" data-start="{" data-end="}">
<div class="line"><a id="l00882" name="l00882"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_c_s.html#a8de556a5e4be31c01350c6b0c125e17e">  882</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_c_s.html#a8de556a5e4be31c01350c6b0c125e17e" title="Solve the sub-problem posed by a single training example.">solveSub</a>(<span class="keywordtype">double</span> epsilon, RealVector&amp; gradient, <span class="keywordtype">double</span> q, <span class="keywordtype">double</span> C, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y, blas::dense_vector_adaptor&lt;double&gt;&amp; alpha, RealVector&amp; mu)</div>
<div class="line"><a id="l00883" name="l00883"></a><span class="lineno">  883</span>    {</div>
<div class="line"><a id="l00884" name="l00884"></a><span class="lineno">  884</span>        <span class="keyword">const</span> <span class="keywordtype">double</span> qq = 0.5 * q;</div>
<div class="line"><a id="l00885" name="l00885"></a><span class="lineno">  885</span>        <span class="keywordtype">double</span> gain = 0.0;</div>
<div class="line"><a id="l00886" name="l00886"></a><span class="lineno">  886</span> </div>
<div class="line"><a id="l00887" name="l00887"></a><span class="lineno">  887</span>        <span class="comment">// SMO loop</span></div>
<div class="line"><a id="l00888" name="l00888"></a><span class="lineno">  888</span>        <span class="keywordtype">size_t</span> iter, maxiter = 10 * <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l00889" name="l00889"></a><span class="lineno">  889</span>        <span class="keywordflow">for</span> (iter=0; iter&lt;maxiter; iter++)</div>
<div class="line"><a id="l00890" name="l00890"></a><span class="lineno">  890</span>        {</div>
<div class="line"><a id="l00891" name="l00891"></a><span class="lineno">  891</span>            <span class="comment">// select working set</span></div>
<div class="line"><a id="l00892" name="l00892"></a><span class="lineno">  892</span>            std::size_t idx = 0;</div>
<div class="line"><a id="l00893" name="l00893"></a><span class="lineno">  893</span>            std::size_t idx_up = 0, idx_down = 0;</div>
<div class="line"><a id="l00894" name="l00894"></a><span class="lineno">  894</span>            <span class="keywordtype">bool</span> size2 = <span class="keyword">false</span>;</div>
<div class="line"><a id="l00895" name="l00895"></a><span class="lineno">  895</span>            <span class="keywordtype">double</span> kkt = 0.0;</div>
<div class="line"><a id="l00896" name="l00896"></a><span class="lineno">  896</span>            <span class="keywordtype">double</span> grad = 0.0;</div>
<div class="line"><a id="l00897" name="l00897"></a><span class="lineno">  897</span>            <span class="keywordflow">if</span> (alpha(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>) == C)</div>
<div class="line"><a id="l00898" name="l00898"></a><span class="lineno">  898</span>            {</div>
<div class="line"><a id="l00899" name="l00899"></a><span class="lineno">  899</span>                <span class="keywordtype">double</span> kkt_up = -1e100, kkt_down = 1e100;</div>
<div class="line"><a id="l00900" name="l00900"></a><span class="lineno">  900</span>                <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++)</div>
<div class="line"><a id="l00901" name="l00901"></a><span class="lineno">  901</span>                {</div>
<div class="line"><a id="l00902" name="l00902"></a><span class="lineno">  902</span>                    <span class="keywordflow">if</span> (c == y) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00903" name="l00903"></a><span class="lineno">  903</span> </div>
<div class="line"><a id="l00904" name="l00904"></a><span class="lineno">  904</span>                    <span class="keyword">const</span> <span class="keywordtype">double</span> g = gradient(c);</div>
<div class="line"><a id="l00905" name="l00905"></a><span class="lineno">  905</span>                    <span class="keyword">const</span> <span class="keywordtype">double</span> a = alpha(c);</div>
<div class="line"><a id="l00906" name="l00906"></a><span class="lineno">  906</span>                    <span class="keywordflow">if</span> (g &gt; kkt_up &amp;&amp; a &lt; C) { kkt_up = g; idx_up = c; }</div>
<div class="line"><a id="l00907" name="l00907"></a><span class="lineno">  907</span>                    <span class="keywordflow">if</span> (g &lt; kkt_down &amp;&amp; a &gt; 0.0) { kkt_down = g; idx_down = c; }</div>
<div class="line"><a id="l00908" name="l00908"></a><span class="lineno">  908</span>                }</div>
<div class="line"><a id="l00909" name="l00909"></a><span class="lineno">  909</span> </div>
<div class="line"><a id="l00910" name="l00910"></a><span class="lineno">  910</span>                <span class="keywordflow">if</span> (kkt_up &lt;= 0.0)</div>
<div class="line"><a id="l00911" name="l00911"></a><span class="lineno">  911</span>                {</div>
<div class="line"><a id="l00912" name="l00912"></a><span class="lineno">  912</span>                    idx = idx_down;</div>
<div class="line"><a id="l00913" name="l00913"></a><span class="lineno">  913</span>                    grad = kkt_down;</div>
<div class="line"><a id="l00914" name="l00914"></a><span class="lineno">  914</span>                    kkt = -kkt_down;</div>
<div class="line"><a id="l00915" name="l00915"></a><span class="lineno">  915</span>                }</div>
<div class="line"><a id="l00916" name="l00916"></a><span class="lineno">  916</span>                <span class="keywordflow">else</span></div>
<div class="line"><a id="l00917" name="l00917"></a><span class="lineno">  917</span>                {</div>
<div class="line"><a id="l00918" name="l00918"></a><span class="lineno">  918</span>                    grad = kkt_up - kkt_down;</div>
<div class="line"><a id="l00919" name="l00919"></a><span class="lineno">  919</span>                    kkt = grad;</div>
<div class="line"><a id="l00920" name="l00920"></a><span class="lineno">  920</span>                    size2 = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00921" name="l00921"></a><span class="lineno">  921</span>                }</div>
<div class="line"><a id="l00922" name="l00922"></a><span class="lineno">  922</span>            }</div>
<div class="line"><a id="l00923" name="l00923"></a><span class="lineno">  923</span>            <span class="keywordflow">else</span></div>
<div class="line"><a id="l00924" name="l00924"></a><span class="lineno">  924</span>            {</div>
<div class="line"><a id="l00925" name="l00925"></a><span class="lineno">  925</span>                <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++)</div>
<div class="line"><a id="l00926" name="l00926"></a><span class="lineno">  926</span>                {</div>
<div class="line"><a id="l00927" name="l00927"></a><span class="lineno">  927</span>                    <span class="keywordflow">if</span> (c == y) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00928" name="l00928"></a><span class="lineno">  928</span> </div>
<div class="line"><a id="l00929" name="l00929"></a><span class="lineno">  929</span>                    <span class="keyword">const</span> <span class="keywordtype">double</span> g = gradient(c);</div>
<div class="line"><a id="l00930" name="l00930"></a><span class="lineno">  930</span>                    <span class="keyword">const</span> <span class="keywordtype">double</span> a = alpha(c);</div>
<div class="line"><a id="l00931" name="l00931"></a><span class="lineno">  931</span>                    <span class="keywordflow">if</span> (g &gt; kkt) { kkt = g; idx = c; }</div>
<div class="line"><a id="l00932" name="l00932"></a><span class="lineno">  932</span>                    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (-g &gt; kkt &amp;&amp; a &gt; 0.0) { kkt = -g; idx = c; }</div>
<div class="line"><a id="l00933" name="l00933"></a><span class="lineno">  933</span>                }</div>
<div class="line"><a id="l00934" name="l00934"></a><span class="lineno">  934</span>                grad = gradient(idx);</div>
<div class="line"><a id="l00935" name="l00935"></a><span class="lineno">  935</span>            }</div>
<div class="line"><a id="l00936" name="l00936"></a><span class="lineno">  936</span> </div>
<div class="line"><a id="l00937" name="l00937"></a><span class="lineno">  937</span>            <span class="comment">// check stopping criterion</span></div>
<div class="line"><a id="l00938" name="l00938"></a><span class="lineno">  938</span>            <span class="keywordflow">if</span> (kkt &lt; epsilon) <span class="keywordflow">return</span> gain;</div>
<div class="line"><a id="l00939" name="l00939"></a><span class="lineno">  939</span> </div>
<div class="line"><a id="l00940" name="l00940"></a><span class="lineno">  940</span>            <span class="keywordflow">if</span> (size2)</div>
<div class="line"><a id="l00941" name="l00941"></a><span class="lineno">  941</span>            {</div>
<div class="line"><a id="l00942" name="l00942"></a><span class="lineno">  942</span>                <span class="comment">// perform step</span></div>
<div class="line"><a id="l00943" name="l00943"></a><span class="lineno">  943</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> a_up = alpha(idx_up);</div>
<div class="line"><a id="l00944" name="l00944"></a><span class="lineno">  944</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> a_down = alpha(idx_down);</div>
<div class="line"><a id="l00945" name="l00945"></a><span class="lineno">  945</span>                <span class="keywordtype">double</span> m = grad / qq;</div>
<div class="line"><a id="l00946" name="l00946"></a><span class="lineno">  946</span>                <span class="keywordtype">double</span> a_up_new = a_up + m;</div>
<div class="line"><a id="l00947" name="l00947"></a><span class="lineno">  947</span>                <span class="keywordtype">double</span> a_down_new = a_down - m;</div>
<div class="line"><a id="l00948" name="l00948"></a><span class="lineno">  948</span>                <span class="keywordflow">if</span> (a_down_new &lt;= 0.0)</div>
<div class="line"><a id="l00949" name="l00949"></a><span class="lineno">  949</span>                {</div>
<div class="line"><a id="l00950" name="l00950"></a><span class="lineno">  950</span>                    m = a_down;</div>
<div class="line"><a id="l00951" name="l00951"></a><span class="lineno">  951</span>                    a_up_new = a_up + m;</div>
<div class="line"><a id="l00952" name="l00952"></a><span class="lineno">  952</span>                    a_down_new = 0.0;</div>
<div class="line"><a id="l00953" name="l00953"></a><span class="lineno">  953</span>                }</div>
<div class="line"><a id="l00954" name="l00954"></a><span class="lineno">  954</span>                alpha(idx_up) = a_up_new;</div>
<div class="line"><a id="l00955" name="l00955"></a><span class="lineno">  955</span>                alpha(idx_down) = a_down_new;</div>
<div class="line"><a id="l00956" name="l00956"></a><span class="lineno">  956</span>                mu(idx_up) += m;</div>
<div class="line"><a id="l00957" name="l00957"></a><span class="lineno">  957</span>                mu(idx_down) -= m;</div>
<div class="line"><a id="l00958" name="l00958"></a><span class="lineno">  958</span> </div>
<div class="line"><a id="l00959" name="l00959"></a><span class="lineno">  959</span>                <span class="comment">// update gradient and total gain</span></div>
<div class="line"><a id="l00960" name="l00960"></a><span class="lineno">  960</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> dg = 0.5 * m * qq;</div>
<div class="line"><a id="l00961" name="l00961"></a><span class="lineno">  961</span>                gradient(idx_up) -= dg;</div>
<div class="line"><a id="l00962" name="l00962"></a><span class="lineno">  962</span>                gradient(idx_down) += dg;</div>
<div class="line"><a id="l00963" name="l00963"></a><span class="lineno">  963</span>                gain += m * (grad - 2.0 * dg);</div>
<div class="line"><a id="l00964" name="l00964"></a><span class="lineno">  964</span>            }</div>
<div class="line"><a id="l00965" name="l00965"></a><span class="lineno">  965</span>            <span class="keywordflow">else</span></div>
<div class="line"><a id="l00966" name="l00966"></a><span class="lineno">  966</span>            {</div>
<div class="line"><a id="l00967" name="l00967"></a><span class="lineno">  967</span>                <span class="comment">// perform step</span></div>
<div class="line"><a id="l00968" name="l00968"></a><span class="lineno">  968</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> a = alpha(idx);</div>
<div class="line"><a id="l00969" name="l00969"></a><span class="lineno">  969</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> a_sum = alpha(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>);</div>
<div class="line"><a id="l00970" name="l00970"></a><span class="lineno">  970</span>                <span class="keywordtype">double</span> m = grad / qq;</div>
<div class="line"><a id="l00971" name="l00971"></a><span class="lineno">  971</span>                <span class="keywordtype">double</span> a_new = a + m;</div>
<div class="line"><a id="l00972" name="l00972"></a><span class="lineno">  972</span>                <span class="keywordtype">double</span> a_sum_new = a_sum + m;</div>
<div class="line"><a id="l00973" name="l00973"></a><span class="lineno">  973</span>                <span class="keywordflow">if</span> (a_new &lt;= 0.0)</div>
<div class="line"><a id="l00974" name="l00974"></a><span class="lineno">  974</span>                {</div>
<div class="line"><a id="l00975" name="l00975"></a><span class="lineno">  975</span>                    m = -a;</div>
<div class="line"><a id="l00976" name="l00976"></a><span class="lineno">  976</span>                    a_new = 0.0;</div>
<div class="line"><a id="l00977" name="l00977"></a><span class="lineno">  977</span>                    a_sum_new = a_sum + m;</div>
<div class="line"><a id="l00978" name="l00978"></a><span class="lineno">  978</span>                }</div>
<div class="line"><a id="l00979" name="l00979"></a><span class="lineno">  979</span>                <span class="keywordflow">else</span> <span class="keywordflow">if</span> (a_sum_new &gt;= C)</div>
<div class="line"><a id="l00980" name="l00980"></a><span class="lineno">  980</span>                {</div>
<div class="line"><a id="l00981" name="l00981"></a><span class="lineno">  981</span>                    m = C - a_sum;</div>
<div class="line"><a id="l00982" name="l00982"></a><span class="lineno">  982</span>                    a_sum_new = C;</div>
<div class="line"><a id="l00983" name="l00983"></a><span class="lineno">  983</span>                    a_new = a + m;</div>
<div class="line"><a id="l00984" name="l00984"></a><span class="lineno">  984</span>                }</div>
<div class="line"><a id="l00985" name="l00985"></a><span class="lineno">  985</span>                alpha(idx) = a_new;</div>
<div class="line"><a id="l00986" name="l00986"></a><span class="lineno">  986</span>                alpha(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>) = a_sum_new;</div>
<div class="line"><a id="l00987" name="l00987"></a><span class="lineno">  987</span>                mu(idx) += m;</div>
<div class="line"><a id="l00988" name="l00988"></a><span class="lineno">  988</span> </div>
<div class="line"><a id="l00989" name="l00989"></a><span class="lineno">  989</span>                <span class="comment">// update gradient and total gain</span></div>
<div class="line"><a id="l00990" name="l00990"></a><span class="lineno">  990</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> dg = 0.5 * m * qq;</div>
<div class="line"><a id="l00991" name="l00991"></a><span class="lineno">  991</span>                <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) gradient(c) -= dg;</div>
<div class="line"><a id="l00992" name="l00992"></a><span class="lineno">  992</span>                gradient(idx) -= dg;</div>
<div class="line"><a id="l00993" name="l00993"></a><span class="lineno">  993</span>                gain += m * (grad - dg);</div>
<div class="line"><a id="l00994" name="l00994"></a><span class="lineno">  994</span>            }</div>
<div class="line"><a id="l00995" name="l00995"></a><span class="lineno">  995</span>        }</div>
<div class="line"><a id="l00996" name="l00996"></a><span class="lineno">  996</span> </div>
<div class="line"><a id="l00997" name="l00997"></a><span class="lineno">  997</span>        <span class="keywordflow">return</span> gain;</div>
<div class="line"><a id="l00998" name="l00998"></a><span class="lineno">  998</span>    }</div>
</div>
<div class="line"><a id="l00999" name="l00999"></a><span class="lineno">  999</span> </div>
<div class="line"><a id="l01000" name="l01000"></a><span class="lineno"> 1000</span><span class="keyword">protected</span>:</div>
<div class="line"><a id="l01001" name="l01001"></a><span class="lineno"> 1001</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#a64edc8279169777bf9ef05052a412acd">::add_scaled</a>;</div>
<div class="line"><a id="l01002" name="l01002"></a><span class="lineno"> 1002</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">::m_data</a>;</div>
<div class="line"><a id="l01003" name="l01003"></a><span class="lineno"> 1003</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">::m_classes</a>;</div>
<div class="line"><a id="l01004" name="l01004"></a><span class="lineno"> 1004</span>};</div>
</div>
<div class="line"><a id="l01005" name="l01005"></a><span class="lineno"> 1005</span> </div>
<div class="line"><a id="l01006" name="l01006"></a><span class="lineno"> 1006</span><span class="comment"></span> </div>
<div class="line"><a id="l01007" name="l01007"></a><span class="lineno"> 1007</span><span class="comment">/// \brief Solver for the multi-class SVM with absolute margin and discriminative maximum loss.</span></div>
<div class="line"><a id="l01008" name="l01008"></a><span class="lineno"> 1008</span><span class="comment"></span><span class="keyword">template</span> &lt;<span class="keyword">class</span> InputT&gt;</div>
<div class="foldopen" id="foldopen01009" data-start="{" data-end="};">
<div class="line"><a id="l01009" name="l01009"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_a_d_m.html"> 1009</a></span><span class="keyword">class </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear_a_d_m.html" title="Solver for the multi-class SVM with absolute margin and discriminative maximum loss.">QpMcLinearADM</a> : <span class="keyword">public</span> <a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;</div>
<div class="line"><a id="l01010" name="l01010"></a><span class="lineno"> 1010</span>{</div>
<div class="line"><a id="l01011" name="l01011"></a><span class="lineno"> 1011</span><span class="keyword">public</span>:</div>
<div class="line"><a id="l01012" name="l01012"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_a_d_m.html#a4d8bc5efdd4db624d7c22a167637e53c"> 1012</a></span>    <span class="keyword">typedef</span> <a class="code hl_class" href="classshark_1_1_labeled_data.html" title="Data set for supervised learning.">LabeledData&lt;InputT, unsigned int&gt;</a> <a class="code hl_typedef" href="classshark_1_1_qp_mc_linear_a_d_m.html#a4d8bc5efdd4db624d7c22a167637e53c">DatasetType</a>;</div>
<div class="line"><a id="l01013" name="l01013"></a><span class="lineno"> 1013</span><span class="comment"></span> </div>
<div class="line"><a id="l01014" name="l01014"></a><span class="lineno"> 1014</span><span class="comment">    /// \brief Constructor</span></div>
<div class="foldopen" id="foldopen01015" data-start="{" data-end="}">
<div class="line"><a id="l01015" name="l01015"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_a_d_m.html#a6066f28f061d4bef949314816c67a82c"> 1015</a></span><span class="comment"></span>    <a class="code hl_function" href="classshark_1_1_qp_mc_linear_a_d_m.html#a6066f28f061d4bef949314816c67a82c" title="Constructor.">QpMcLinearADM</a>(</div>
<div class="line"><a id="l01016" name="l01016"></a><span class="lineno"> 1016</span>            <span class="keyword">const</span> <a class="code hl_class" href="classshark_1_1_labeled_data.html" title="Data set for supervised learning.">DatasetType</a>&amp; dataset,</div>
<div class="line"><a id="l01017" name="l01017"></a><span class="lineno"> 1017</span>            std::size_t dim,</div>
<div class="line"><a id="l01018" name="l01018"></a><span class="lineno"> 1018</span>            std::size_t classes)</div>
<div class="line"><a id="l01019" name="l01019"></a><span class="lineno"> 1019</span>    : <a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;(dataset, dim, classes)</div>
<div class="line"><a id="l01020" name="l01020"></a><span class="lineno"> 1020</span>    { }</div>
</div>
<div class="line"><a id="l01021" name="l01021"></a><span class="lineno"> 1021</span> </div>
<div class="line"><a id="l01022" name="l01022"></a><span class="lineno"> 1022</span><span class="keyword">protected</span>:<span class="comment"></span></div>
<div class="line"><a id="l01023" name="l01023"></a><span class="lineno"> 1023</span><span class="comment">    /// \brief Compute the gradient from the inner products of the weight vectors with the current sample.</span></div>
<div class="foldopen" id="foldopen01024" data-start="{" data-end="}">
<div class="line"><a id="l01024" name="l01024"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_a_d_m.html#af8021dbbe5f3c4b3e5fdc83b941748cd"> 1024</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_a_d_m.html#af8021dbbe5f3c4b3e5fdc83b941748cd" title="Compute the gradient from the inner products of the weight vectors with the current sample.">calcGradient</a>(RealVector&amp; gradient, RealVector wx, blas::dense_vector_adaptor&lt;double const&gt; <span class="keyword">const</span>&amp; alpha, <span class="keywordtype">double</span> C, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y)</div>
<div class="line"><a id="l01025" name="l01025"></a><span class="lineno"> 1025</span>    {</div>
<div class="line"><a id="l01026" name="l01026"></a><span class="lineno"> 1026</span>        <span class="keywordflow">if</span> (alpha(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>) &lt; C)</div>
<div class="line"><a id="l01027" name="l01027"></a><span class="lineno"> 1027</span>        {</div>
<div class="line"><a id="l01028" name="l01028"></a><span class="lineno"> 1028</span>            <span class="keywordtype">double</span> violation = 0.0;</div>
<div class="line"><a id="l01029" name="l01029"></a><span class="lineno"> 1029</span>            <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++)</div>
<div class="line"><a id="l01030" name="l01030"></a><span class="lineno"> 1030</span>            {</div>
<div class="line"><a id="l01031" name="l01031"></a><span class="lineno"> 1031</span>                <span class="keywordflow">if</span> (c == y)</div>
<div class="line"><a id="l01032" name="l01032"></a><span class="lineno"> 1032</span>                {</div>
<div class="line"><a id="l01033" name="l01033"></a><span class="lineno"> 1033</span>                    gradient(c) = 0.0;</div>
<div class="line"><a id="l01034" name="l01034"></a><span class="lineno"> 1034</span>                }</div>
<div class="line"><a id="l01035" name="l01035"></a><span class="lineno"> 1035</span>                <span class="keywordflow">else</span></div>
<div class="line"><a id="l01036" name="l01036"></a><span class="lineno"> 1036</span>                {</div>
<div class="line"><a id="l01037" name="l01037"></a><span class="lineno"> 1037</span>                    <span class="keyword">const</span> <span class="keywordtype">double</span> g = 1.0 + wx(c);</div>
<div class="line"><a id="l01038" name="l01038"></a><span class="lineno"> 1038</span>                    gradient(c) = g;</div>
<div class="line"><a id="l01039" name="l01039"></a><span class="lineno"> 1039</span>                    <span class="keywordflow">if</span> (g &gt; violation) violation = g;</div>
<div class="line"><a id="l01040" name="l01040"></a><span class="lineno"> 1040</span>                    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (-g &gt; violation &amp;&amp; alpha(c) &gt; 0.0) violation = -g;</div>
<div class="line"><a id="l01041" name="l01041"></a><span class="lineno"> 1041</span>                }</div>
<div class="line"><a id="l01042" name="l01042"></a><span class="lineno"> 1042</span>            }</div>
<div class="line"><a id="l01043" name="l01043"></a><span class="lineno"> 1043</span>            <span class="keywordflow">return</span> violation;</div>
<div class="line"><a id="l01044" name="l01044"></a><span class="lineno"> 1044</span>        }</div>
<div class="line"><a id="l01045" name="l01045"></a><span class="lineno"> 1045</span>        <span class="keywordflow">else</span></div>
<div class="line"><a id="l01046" name="l01046"></a><span class="lineno"> 1046</span>        {</div>
<div class="line"><a id="l01047" name="l01047"></a><span class="lineno"> 1047</span>            <span class="keywordtype">double</span> kkt_up = 0.0, kkt_down = 1e100;</div>
<div class="line"><a id="l01048" name="l01048"></a><span class="lineno"> 1048</span>            <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++)</div>
<div class="line"><a id="l01049" name="l01049"></a><span class="lineno"> 1049</span>            {</div>
<div class="line"><a id="l01050" name="l01050"></a><span class="lineno"> 1050</span>                <span class="keywordflow">if</span> (c == y)</div>
<div class="line"><a id="l01051" name="l01051"></a><span class="lineno"> 1051</span>                {</div>
<div class="line"><a id="l01052" name="l01052"></a><span class="lineno"> 1052</span>                    gradient(c) = 0.0;</div>
<div class="line"><a id="l01053" name="l01053"></a><span class="lineno"> 1053</span>                }</div>
<div class="line"><a id="l01054" name="l01054"></a><span class="lineno"> 1054</span>                <span class="keywordflow">else</span></div>
<div class="line"><a id="l01055" name="l01055"></a><span class="lineno"> 1055</span>                {</div>
<div class="line"><a id="l01056" name="l01056"></a><span class="lineno"> 1056</span>                    <span class="keyword">const</span> <span class="keywordtype">double</span> g = 1.0 + wx(c);</div>
<div class="line"><a id="l01057" name="l01057"></a><span class="lineno"> 1057</span>                    gradient(c) = g;</div>
<div class="line"><a id="l01058" name="l01058"></a><span class="lineno"> 1058</span>                    <span class="keywordflow">if</span> (g &gt; kkt_up &amp;&amp; alpha(c) &lt; C) kkt_up = g;</div>
<div class="line"><a id="l01059" name="l01059"></a><span class="lineno"> 1059</span>                    <span class="keywordflow">if</span> (g &lt; kkt_down &amp;&amp; alpha(c) &gt; 0.0) kkt_down = g;</div>
<div class="line"><a id="l01060" name="l01060"></a><span class="lineno"> 1060</span>                }</div>
<div class="line"><a id="l01061" name="l01061"></a><span class="lineno"> 1061</span>            }</div>
<div class="line"><a id="l01062" name="l01062"></a><span class="lineno"> 1062</span>            <span class="keywordflow">return</span> std::max(0.0, kkt_up - kkt_down);</div>
<div class="line"><a id="l01063" name="l01063"></a><span class="lineno"> 1063</span>        }</div>
<div class="line"><a id="l01064" name="l01064"></a><span class="lineno"> 1064</span>    }</div>
</div>
<div class="line"><a id="l01065" name="l01065"></a><span class="lineno"> 1065</span><span class="comment"></span> </div>
<div class="line"><a id="l01066" name="l01066"></a><span class="lineno"> 1066</span><span class="comment">    /// \brief Update the weight vectors (primal variables) after a step on the dual variables.</span></div>
<div class="foldopen" id="foldopen01067" data-start="{" data-end="}">
<div class="line"><a id="l01067" name="l01067"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_a_d_m.html#ad9c79ecd1418beba9c94b414a8f3b8ef"> 1067</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_a_d_m.html#ad9c79ecd1418beba9c94b414a8f3b8ef" title="Update the weight vectors (primal variables) after a step on the dual variables.">updateWeightVectors</a>(RealMatrix&amp; w, RealVector <span class="keyword">const</span>&amp; mu, std::size_t index)</div>
<div class="line"><a id="l01068" name="l01068"></a><span class="lineno"> 1068</span>    {</div>
<div class="line"><a id="l01069" name="l01069"></a><span class="lineno"> 1069</span>        <span class="keywordtype">double</span> mean_mu = 0.0;</div>
<div class="line"><a id="l01070" name="l01070"></a><span class="lineno"> 1070</span>        <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) mean_mu += mu(c);</div>
<div class="line"><a id="l01071" name="l01071"></a><span class="lineno"> 1071</span>        mean_mu /= (double)<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l01072" name="l01072"></a><span class="lineno"> 1072</span>        RealVector step(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>);</div>
<div class="line"><a id="l01073" name="l01073"></a><span class="lineno"> 1073</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) step(c) = mean_mu - mu(c);</div>
<div class="line"><a id="l01074" name="l01074"></a><span class="lineno"> 1074</span>        <a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#a64edc8279169777bf9ef05052a412acd">add_scaled</a>(w, step, <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">m_data</a>[index].input);</div>
<div class="line"><a id="l01075" name="l01075"></a><span class="lineno"> 1075</span>    }</div>
</div>
<div class="line"><a id="l01076" name="l01076"></a><span class="lineno"> 1076</span><span class="comment"></span> </div>
<div class="line"><a id="l01077" name="l01077"></a><span class="lineno"> 1077</span><span class="comment">    /// \brief Solve the sub-problem posed by a single training example.</span></div>
<div class="foldopen" id="foldopen01078" data-start="{" data-end="}">
<div class="line"><a id="l01078" name="l01078"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_a_d_m.html#a81cde691765509bedeafe49950a4f55f"> 1078</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_a_d_m.html#a81cde691765509bedeafe49950a4f55f" title="Solve the sub-problem posed by a single training example.">solveSub</a>(<span class="keywordtype">double</span> epsilon, RealVector&amp; gradient, <span class="keywordtype">double</span> q, <span class="keywordtype">double</span> C, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y, blas::dense_vector_adaptor&lt;double&gt;&amp; alpha, RealVector&amp; mu)</div>
<div class="line"><a id="l01079" name="l01079"></a><span class="lineno"> 1079</span>    {</div>
<div class="line"><a id="l01080" name="l01080"></a><span class="lineno"> 1080</span>        <span class="keyword">const</span> <span class="keywordtype">double</span> ood = 1.0 / <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l01081" name="l01081"></a><span class="lineno"> 1081</span>        <span class="keyword">const</span> <span class="keywordtype">double</span> qq = (1.0 - ood) * q;</div>
<div class="line"><a id="l01082" name="l01082"></a><span class="lineno"> 1082</span>        <span class="keywordtype">double</span> gain = 0.0;</div>
<div class="line"><a id="l01083" name="l01083"></a><span class="lineno"> 1083</span> </div>
<div class="line"><a id="l01084" name="l01084"></a><span class="lineno"> 1084</span>        <span class="comment">// SMO loop</span></div>
<div class="line"><a id="l01085" name="l01085"></a><span class="lineno"> 1085</span>        <span class="keywordtype">size_t</span> iter, maxiter = 10 * <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l01086" name="l01086"></a><span class="lineno"> 1086</span>        <span class="keywordflow">for</span> (iter=0; iter&lt;maxiter; iter++)</div>
<div class="line"><a id="l01087" name="l01087"></a><span class="lineno"> 1087</span>        {</div>
<div class="line"><a id="l01088" name="l01088"></a><span class="lineno"> 1088</span>            <span class="comment">// select working set</span></div>
<div class="line"><a id="l01089" name="l01089"></a><span class="lineno"> 1089</span>            std::size_t idx = 0;</div>
<div class="line"><a id="l01090" name="l01090"></a><span class="lineno"> 1090</span>            std::size_t idx_up = 0, idx_down = 0;</div>
<div class="line"><a id="l01091" name="l01091"></a><span class="lineno"> 1091</span>            <span class="keywordtype">bool</span> size2 = <span class="keyword">false</span>;</div>
<div class="line"><a id="l01092" name="l01092"></a><span class="lineno"> 1092</span>            <span class="keywordtype">double</span> kkt = 0.0;</div>
<div class="line"><a id="l01093" name="l01093"></a><span class="lineno"> 1093</span>            <span class="keywordtype">double</span> grad = 0.0;</div>
<div class="line"><a id="l01094" name="l01094"></a><span class="lineno"> 1094</span>            <span class="keywordflow">if</span> (alpha(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>) == C)</div>
<div class="line"><a id="l01095" name="l01095"></a><span class="lineno"> 1095</span>            {</div>
<div class="line"><a id="l01096" name="l01096"></a><span class="lineno"> 1096</span>                <span class="keywordtype">double</span> kkt_up = -1e100, kkt_down = 1e100;</div>
<div class="line"><a id="l01097" name="l01097"></a><span class="lineno"> 1097</span>                <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++)</div>
<div class="line"><a id="l01098" name="l01098"></a><span class="lineno"> 1098</span>                {</div>
<div class="line"><a id="l01099" name="l01099"></a><span class="lineno"> 1099</span>                    <span class="keywordflow">if</span> (c == y) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l01100" name="l01100"></a><span class="lineno"> 1100</span> </div>
<div class="line"><a id="l01101" name="l01101"></a><span class="lineno"> 1101</span>                    <span class="keyword">const</span> <span class="keywordtype">double</span> g = gradient(c);</div>
<div class="line"><a id="l01102" name="l01102"></a><span class="lineno"> 1102</span>                    <span class="keyword">const</span> <span class="keywordtype">double</span> a = alpha(c);</div>
<div class="line"><a id="l01103" name="l01103"></a><span class="lineno"> 1103</span>                    <span class="keywordflow">if</span> (g &gt; kkt_up &amp;&amp; a &lt; C) { kkt_up = g; idx_up = c; }</div>
<div class="line"><a id="l01104" name="l01104"></a><span class="lineno"> 1104</span>                    <span class="keywordflow">if</span> (g &lt; kkt_down &amp;&amp; a &gt; 0.0) { kkt_down = g; idx_down = c; }</div>
<div class="line"><a id="l01105" name="l01105"></a><span class="lineno"> 1105</span>                }</div>
<div class="line"><a id="l01106" name="l01106"></a><span class="lineno"> 1106</span> </div>
<div class="line"><a id="l01107" name="l01107"></a><span class="lineno"> 1107</span>                <span class="keywordflow">if</span> (kkt_up &lt;= 0.0)</div>
<div class="line"><a id="l01108" name="l01108"></a><span class="lineno"> 1108</span>                {</div>
<div class="line"><a id="l01109" name="l01109"></a><span class="lineno"> 1109</span>                    idx = idx_down;</div>
<div class="line"><a id="l01110" name="l01110"></a><span class="lineno"> 1110</span>                    grad = kkt_down;</div>
<div class="line"><a id="l01111" name="l01111"></a><span class="lineno"> 1111</span>                    kkt = -kkt_down;</div>
<div class="line"><a id="l01112" name="l01112"></a><span class="lineno"> 1112</span>                }</div>
<div class="line"><a id="l01113" name="l01113"></a><span class="lineno"> 1113</span>                <span class="keywordflow">else</span></div>
<div class="line"><a id="l01114" name="l01114"></a><span class="lineno"> 1114</span>                {</div>
<div class="line"><a id="l01115" name="l01115"></a><span class="lineno"> 1115</span>                    grad = kkt_up - kkt_down;</div>
<div class="line"><a id="l01116" name="l01116"></a><span class="lineno"> 1116</span>                    kkt = grad;</div>
<div class="line"><a id="l01117" name="l01117"></a><span class="lineno"> 1117</span>                    size2 = <span class="keyword">true</span>;</div>
<div class="line"><a id="l01118" name="l01118"></a><span class="lineno"> 1118</span>                }</div>
<div class="line"><a id="l01119" name="l01119"></a><span class="lineno"> 1119</span>            }</div>
<div class="line"><a id="l01120" name="l01120"></a><span class="lineno"> 1120</span>            <span class="keywordflow">else</span></div>
<div class="line"><a id="l01121" name="l01121"></a><span class="lineno"> 1121</span>            {</div>
<div class="line"><a id="l01122" name="l01122"></a><span class="lineno"> 1122</span>                <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++)</div>
<div class="line"><a id="l01123" name="l01123"></a><span class="lineno"> 1123</span>                {</div>
<div class="line"><a id="l01124" name="l01124"></a><span class="lineno"> 1124</span>                    <span class="keywordflow">if</span> (c == y) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l01125" name="l01125"></a><span class="lineno"> 1125</span> </div>
<div class="line"><a id="l01126" name="l01126"></a><span class="lineno"> 1126</span>                    <span class="keyword">const</span> <span class="keywordtype">double</span> g = gradient(c);</div>
<div class="line"><a id="l01127" name="l01127"></a><span class="lineno"> 1127</span>                    <span class="keyword">const</span> <span class="keywordtype">double</span> a = alpha(c);</div>
<div class="line"><a id="l01128" name="l01128"></a><span class="lineno"> 1128</span>                    <span class="keywordflow">if</span> (g &gt; kkt) { kkt = g; idx = c; }</div>
<div class="line"><a id="l01129" name="l01129"></a><span class="lineno"> 1129</span>                    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (-g &gt; kkt &amp;&amp; a &gt; 0.0) { kkt = -g; idx = c; }</div>
<div class="line"><a id="l01130" name="l01130"></a><span class="lineno"> 1130</span>                }</div>
<div class="line"><a id="l01131" name="l01131"></a><span class="lineno"> 1131</span>                grad = gradient(idx);</div>
<div class="line"><a id="l01132" name="l01132"></a><span class="lineno"> 1132</span>            }</div>
<div class="line"><a id="l01133" name="l01133"></a><span class="lineno"> 1133</span> </div>
<div class="line"><a id="l01134" name="l01134"></a><span class="lineno"> 1134</span>            <span class="comment">// check stopping criterion</span></div>
<div class="line"><a id="l01135" name="l01135"></a><span class="lineno"> 1135</span>            <span class="keywordflow">if</span> (kkt &lt; epsilon) <span class="keywordflow">return</span> gain;</div>
<div class="line"><a id="l01136" name="l01136"></a><span class="lineno"> 1136</span> </div>
<div class="line"><a id="l01137" name="l01137"></a><span class="lineno"> 1137</span>            <span class="keywordflow">if</span> (size2)</div>
<div class="line"><a id="l01138" name="l01138"></a><span class="lineno"> 1138</span>            {</div>
<div class="line"><a id="l01139" name="l01139"></a><span class="lineno"> 1139</span>                <span class="comment">// perform step</span></div>
<div class="line"><a id="l01140" name="l01140"></a><span class="lineno"> 1140</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> a_up = alpha(idx_up);</div>
<div class="line"><a id="l01141" name="l01141"></a><span class="lineno"> 1141</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> a_down = alpha(idx_down);</div>
<div class="line"><a id="l01142" name="l01142"></a><span class="lineno"> 1142</span>                <span class="keywordtype">double</span> m = grad / (2.0 * q);</div>
<div class="line"><a id="l01143" name="l01143"></a><span class="lineno"> 1143</span>                <span class="keywordtype">double</span> a_up_new = a_up + m;</div>
<div class="line"><a id="l01144" name="l01144"></a><span class="lineno"> 1144</span>                <span class="keywordtype">double</span> a_down_new = a_down - m;</div>
<div class="line"><a id="l01145" name="l01145"></a><span class="lineno"> 1145</span>                <span class="keywordflow">if</span> (a_down_new &lt;= 0.0)</div>
<div class="line"><a id="l01146" name="l01146"></a><span class="lineno"> 1146</span>                {</div>
<div class="line"><a id="l01147" name="l01147"></a><span class="lineno"> 1147</span>                    m = a_down;</div>
<div class="line"><a id="l01148" name="l01148"></a><span class="lineno"> 1148</span>                    a_up_new = a_up + m;</div>
<div class="line"><a id="l01149" name="l01149"></a><span class="lineno"> 1149</span>                    a_down_new = 0.0;</div>
<div class="line"><a id="l01150" name="l01150"></a><span class="lineno"> 1150</span>                }</div>
<div class="line"><a id="l01151" name="l01151"></a><span class="lineno"> 1151</span>                alpha(idx_up) = a_up_new;</div>
<div class="line"><a id="l01152" name="l01152"></a><span class="lineno"> 1152</span>                alpha(idx_down) = a_down_new;</div>
<div class="line"><a id="l01153" name="l01153"></a><span class="lineno"> 1153</span>                mu(idx_up) += m;</div>
<div class="line"><a id="l01154" name="l01154"></a><span class="lineno"> 1154</span>                mu(idx_down) -= m;</div>
<div class="line"><a id="l01155" name="l01155"></a><span class="lineno"> 1155</span> </div>
<div class="line"><a id="l01156" name="l01156"></a><span class="lineno"> 1156</span>                <span class="comment">// update gradient and total gain</span></div>
<div class="line"><a id="l01157" name="l01157"></a><span class="lineno"> 1157</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> dg = m * q;</div>
<div class="line"><a id="l01158" name="l01158"></a><span class="lineno"> 1158</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> dgc = dg / <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l01159" name="l01159"></a><span class="lineno"> 1159</span>                gradient(idx_up) -= dg;</div>
<div class="line"><a id="l01160" name="l01160"></a><span class="lineno"> 1160</span>                gradient(idx_down) += dg;</div>
<div class="line"><a id="l01161" name="l01161"></a><span class="lineno"> 1161</span>                gain += m * (grad - (dg - dgc));</div>
<div class="line"><a id="l01162" name="l01162"></a><span class="lineno"> 1162</span>            }</div>
<div class="line"><a id="l01163" name="l01163"></a><span class="lineno"> 1163</span>            <span class="keywordflow">else</span></div>
<div class="line"><a id="l01164" name="l01164"></a><span class="lineno"> 1164</span>            {</div>
<div class="line"><a id="l01165" name="l01165"></a><span class="lineno"> 1165</span>                <span class="comment">// perform step</span></div>
<div class="line"><a id="l01166" name="l01166"></a><span class="lineno"> 1166</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> a = alpha(idx);</div>
<div class="line"><a id="l01167" name="l01167"></a><span class="lineno"> 1167</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> a_sum = alpha(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>);</div>
<div class="line"><a id="l01168" name="l01168"></a><span class="lineno"> 1168</span>                <span class="keywordtype">double</span> m = grad / qq;</div>
<div class="line"><a id="l01169" name="l01169"></a><span class="lineno"> 1169</span>                <span class="keywordtype">double</span> a_new = a + m;</div>
<div class="line"><a id="l01170" name="l01170"></a><span class="lineno"> 1170</span>                <span class="keywordtype">double</span> a_sum_new = a_sum + m;</div>
<div class="line"><a id="l01171" name="l01171"></a><span class="lineno"> 1171</span>                <span class="keywordflow">if</span> (a_new &lt;= 0.0)</div>
<div class="line"><a id="l01172" name="l01172"></a><span class="lineno"> 1172</span>                {</div>
<div class="line"><a id="l01173" name="l01173"></a><span class="lineno"> 1173</span>                    m = -a;</div>
<div class="line"><a id="l01174" name="l01174"></a><span class="lineno"> 1174</span>                    a_new = 0.0;</div>
<div class="line"><a id="l01175" name="l01175"></a><span class="lineno"> 1175</span>                    a_sum_new = a_sum + m;</div>
<div class="line"><a id="l01176" name="l01176"></a><span class="lineno"> 1176</span>                }</div>
<div class="line"><a id="l01177" name="l01177"></a><span class="lineno"> 1177</span>                <span class="keywordflow">else</span> <span class="keywordflow">if</span> (a_sum_new &gt;= C)</div>
<div class="line"><a id="l01178" name="l01178"></a><span class="lineno"> 1178</span>                {</div>
<div class="line"><a id="l01179" name="l01179"></a><span class="lineno"> 1179</span>                    m = C - a_sum;</div>
<div class="line"><a id="l01180" name="l01180"></a><span class="lineno"> 1180</span>                    a_sum_new = C;</div>
<div class="line"><a id="l01181" name="l01181"></a><span class="lineno"> 1181</span>                    a_new = a + m;</div>
<div class="line"><a id="l01182" name="l01182"></a><span class="lineno"> 1182</span>                }</div>
<div class="line"><a id="l01183" name="l01183"></a><span class="lineno"> 1183</span>                alpha(idx) = a_new;</div>
<div class="line"><a id="l01184" name="l01184"></a><span class="lineno"> 1184</span>                alpha(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>) = a_sum_new;</div>
<div class="line"><a id="l01185" name="l01185"></a><span class="lineno"> 1185</span>                mu(idx) += m;</div>
<div class="line"><a id="l01186" name="l01186"></a><span class="lineno"> 1186</span> </div>
<div class="line"><a id="l01187" name="l01187"></a><span class="lineno"> 1187</span>                <span class="comment">// update gradient and total gain</span></div>
<div class="line"><a id="l01188" name="l01188"></a><span class="lineno"> 1188</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> dg = m * q;</div>
<div class="line"><a id="l01189" name="l01189"></a><span class="lineno"> 1189</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> dgc = dg / <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l01190" name="l01190"></a><span class="lineno"> 1190</span>                <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) gradient(c) += dgc;</div>
<div class="line"><a id="l01191" name="l01191"></a><span class="lineno"> 1191</span>                gradient(idx) -= dg;</div>
<div class="line"><a id="l01192" name="l01192"></a><span class="lineno"> 1192</span>                gain += m * (grad - 0.5 * (dg - dgc));</div>
<div class="line"><a id="l01193" name="l01193"></a><span class="lineno"> 1193</span>            }</div>
<div class="line"><a id="l01194" name="l01194"></a><span class="lineno"> 1194</span>        }</div>
<div class="line"><a id="l01195" name="l01195"></a><span class="lineno"> 1195</span> </div>
<div class="line"><a id="l01196" name="l01196"></a><span class="lineno"> 1196</span>        <span class="keywordflow">return</span> gain;</div>
<div class="line"><a id="l01197" name="l01197"></a><span class="lineno"> 1197</span>    }</div>
</div>
<div class="line"><a id="l01198" name="l01198"></a><span class="lineno"> 1198</span> </div>
<div class="line"><a id="l01199" name="l01199"></a><span class="lineno"> 1199</span><span class="keyword">protected</span>:</div>
<div class="line"><a id="l01200" name="l01200"></a><span class="lineno"> 1200</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#a64edc8279169777bf9ef05052a412acd">::add_scaled</a>;</div>
<div class="line"><a id="l01201" name="l01201"></a><span class="lineno"> 1201</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">::m_data</a>;</div>
<div class="line"><a id="l01202" name="l01202"></a><span class="lineno"> 1202</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">::m_classes</a>;</div>
<div class="line"><a id="l01203" name="l01203"></a><span class="lineno"> 1203</span>};</div>
</div>
<div class="line"><a id="l01204" name="l01204"></a><span class="lineno"> 1204</span> </div>
<div class="line"><a id="l01205" name="l01205"></a><span class="lineno"> 1205</span><span class="comment"></span> </div>
<div class="line"><a id="l01206" name="l01206"></a><span class="lineno"> 1206</span><span class="comment">/// \brief Solver for the multi-class SVM with absolute margin and total maximum loss.</span></div>
<div class="line"><a id="l01207" name="l01207"></a><span class="lineno"> 1207</span><span class="comment"></span><span class="keyword">template</span> &lt;<span class="keyword">class</span> InputT&gt;</div>
<div class="foldopen" id="foldopen01208" data-start="{" data-end="};">
<div class="line"><a id="l01208" name="l01208"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_a_t_m.html"> 1208</a></span><span class="keyword">class </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear_a_t_m.html" title="Solver for the multi-class SVM with absolute margin and total maximum loss.">QpMcLinearATM</a> : <span class="keyword">public</span> <a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;</div>
<div class="line"><a id="l01209" name="l01209"></a><span class="lineno"> 1209</span>{</div>
<div class="line"><a id="l01210" name="l01210"></a><span class="lineno"> 1210</span><span class="keyword">public</span>:</div>
<div class="line"><a id="l01211" name="l01211"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_a_t_m.html#ab7575e4a5092dac0849da7907d4b1871"> 1211</a></span>    <span class="keyword">typedef</span> <a class="code hl_class" href="classshark_1_1_labeled_data.html" title="Data set for supervised learning.">LabeledData&lt;InputT, unsigned int&gt;</a> <a class="code hl_typedef" href="classshark_1_1_qp_mc_linear_a_t_m.html#ab7575e4a5092dac0849da7907d4b1871">DatasetType</a>;</div>
<div class="line"><a id="l01212" name="l01212"></a><span class="lineno"> 1212</span><span class="comment"></span> </div>
<div class="line"><a id="l01213" name="l01213"></a><span class="lineno"> 1213</span><span class="comment">    /// \brief Constructor</span></div>
<div class="foldopen" id="foldopen01214" data-start="{" data-end="}">
<div class="line"><a id="l01214" name="l01214"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_a_t_m.html#acb93af3d99bdddc6368526cf6adbd0f9"> 1214</a></span><span class="comment"></span>    <a class="code hl_function" href="classshark_1_1_qp_mc_linear_a_t_m.html#acb93af3d99bdddc6368526cf6adbd0f9" title="Constructor.">QpMcLinearATM</a>(</div>
<div class="line"><a id="l01215" name="l01215"></a><span class="lineno"> 1215</span>            <span class="keyword">const</span> <a class="code hl_class" href="classshark_1_1_labeled_data.html" title="Data set for supervised learning.">DatasetType</a>&amp; dataset,</div>
<div class="line"><a id="l01216" name="l01216"></a><span class="lineno"> 1216</span>            std::size_t dim,</div>
<div class="line"><a id="l01217" name="l01217"></a><span class="lineno"> 1217</span>            std::size_t classes)</div>
<div class="line"><a id="l01218" name="l01218"></a><span class="lineno"> 1218</span>    : <a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;(dataset, dim, classes)</div>
<div class="line"><a id="l01219" name="l01219"></a><span class="lineno"> 1219</span>    { }</div>
</div>
<div class="line"><a id="l01220" name="l01220"></a><span class="lineno"> 1220</span> </div>
<div class="line"><a id="l01221" name="l01221"></a><span class="lineno"> 1221</span><span class="keyword">protected</span>:<span class="comment"></span></div>
<div class="line"><a id="l01222" name="l01222"></a><span class="lineno"> 1222</span><span class="comment">    /// \brief Compute the gradient from the inner products of the weight vectors with the current sample.</span></div>
<div class="foldopen" id="foldopen01223" data-start="{" data-end="}">
<div class="line"><a id="l01223" name="l01223"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_a_t_m.html#afe91c0937cc28462d3d6d6dbeca8a52d"> 1223</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_a_t_m.html#afe91c0937cc28462d3d6d6dbeca8a52d" title="Compute the gradient from the inner products of the weight vectors with the current sample.">calcGradient</a>(RealVector&amp; gradient, RealVector wx, blas::dense_vector_adaptor&lt;double const&gt; <span class="keyword">const</span>&amp; alpha, <span class="keywordtype">double</span> C, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y)</div>
<div class="line"><a id="l01224" name="l01224"></a><span class="lineno"> 1224</span>    {</div>
<div class="line"><a id="l01225" name="l01225"></a><span class="lineno"> 1225</span>        <span class="keywordflow">if</span> (alpha(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>) &lt; C)</div>
<div class="line"><a id="l01226" name="l01226"></a><span class="lineno"> 1226</span>        {</div>
<div class="line"><a id="l01227" name="l01227"></a><span class="lineno"> 1227</span>            <span class="keywordtype">double</span> violation = 0.0;</div>
<div class="line"><a id="l01228" name="l01228"></a><span class="lineno"> 1228</span>            <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++)</div>
<div class="line"><a id="l01229" name="l01229"></a><span class="lineno"> 1229</span>            {</div>
<div class="line"><a id="l01230" name="l01230"></a><span class="lineno"> 1230</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> g = (c == y) ? 1.0 - wx(y) : 1.0 + wx(c);</div>
<div class="line"><a id="l01231" name="l01231"></a><span class="lineno"> 1231</span>                gradient(c) = g;</div>
<div class="line"><a id="l01232" name="l01232"></a><span class="lineno"> 1232</span>                <span class="keywordflow">if</span> (g &gt; violation) violation = g;</div>
<div class="line"><a id="l01233" name="l01233"></a><span class="lineno"> 1233</span>                <span class="keywordflow">else</span> <span class="keywordflow">if</span> (-g &gt; violation &amp;&amp; alpha(c) &gt; 0.0) violation = -g;</div>
<div class="line"><a id="l01234" name="l01234"></a><span class="lineno"> 1234</span>            }</div>
<div class="line"><a id="l01235" name="l01235"></a><span class="lineno"> 1235</span>            <span class="keywordflow">return</span> violation;</div>
<div class="line"><a id="l01236" name="l01236"></a><span class="lineno"> 1236</span>        }</div>
<div class="line"><a id="l01237" name="l01237"></a><span class="lineno"> 1237</span>        <span class="keywordflow">else</span></div>
<div class="line"><a id="l01238" name="l01238"></a><span class="lineno"> 1238</span>        {</div>
<div class="line"><a id="l01239" name="l01239"></a><span class="lineno"> 1239</span>            <span class="keywordtype">double</span> kkt_up = 0.0, kkt_down = 1e100;</div>
<div class="line"><a id="l01240" name="l01240"></a><span class="lineno"> 1240</span>            <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++)</div>
<div class="line"><a id="l01241" name="l01241"></a><span class="lineno"> 1241</span>            {</div>
<div class="line"><a id="l01242" name="l01242"></a><span class="lineno"> 1242</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> g = (c == y) ? 1.0 - wx(y) : 1.0 + wx(c);</div>
<div class="line"><a id="l01243" name="l01243"></a><span class="lineno"> 1243</span>                gradient(c) = g;</div>
<div class="line"><a id="l01244" name="l01244"></a><span class="lineno"> 1244</span>                <span class="keywordflow">if</span> (g &gt; kkt_up &amp;&amp; alpha(c) &lt; C) kkt_up = g;</div>
<div class="line"><a id="l01245" name="l01245"></a><span class="lineno"> 1245</span>                <span class="keywordflow">if</span> (g &lt; kkt_down &amp;&amp; alpha(c) &gt; 0.0) kkt_down = g;</div>
<div class="line"><a id="l01246" name="l01246"></a><span class="lineno"> 1246</span>            }</div>
<div class="line"><a id="l01247" name="l01247"></a><span class="lineno"> 1247</span>            <span class="keywordflow">return</span> std::max(0.0, kkt_up - kkt_down);</div>
<div class="line"><a id="l01248" name="l01248"></a><span class="lineno"> 1248</span>        }</div>
<div class="line"><a id="l01249" name="l01249"></a><span class="lineno"> 1249</span>    }</div>
</div>
<div class="line"><a id="l01250" name="l01250"></a><span class="lineno"> 1250</span><span class="comment"></span> </div>
<div class="line"><a id="l01251" name="l01251"></a><span class="lineno"> 1251</span><span class="comment">    /// \brief Update the weight vectors (primal variables) after a step on the dual variables.</span></div>
<div class="foldopen" id="foldopen01252" data-start="{" data-end="}">
<div class="line"><a id="l01252" name="l01252"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_a_t_m.html#ac3cac29e695f9788bcf6406dffee8bfc"> 1252</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_a_t_m.html#ac3cac29e695f9788bcf6406dffee8bfc" title="Update the weight vectors (primal variables) after a step on the dual variables.">updateWeightVectors</a>(RealMatrix&amp; w, RealVector <span class="keyword">const</span>&amp; mu, std::size_t index)</div>
<div class="line"><a id="l01253" name="l01253"></a><span class="lineno"> 1253</span>    {</div>
<div class="line"><a id="l01254" name="l01254"></a><span class="lineno"> 1254</span>        <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y = <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">m_data</a>[index].label;</div>
<div class="line"><a id="l01255" name="l01255"></a><span class="lineno"> 1255</span>        <span class="keywordtype">double</span> <a class="code hl_function" href="namespaceshark.html#a6ae694efca57e84792fcff090223437e" title="Calculates the mean vector of the input vectors.">mean</a> = -2.0 * mu(y);</div>
<div class="line"><a id="l01256" name="l01256"></a><span class="lineno"> 1256</span>        <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) <a class="code hl_function" href="namespaceshark.html#a6ae694efca57e84792fcff090223437e" title="Calculates the mean vector of the input vectors.">mean</a> += mu(c);</div>
<div class="line"><a id="l01257" name="l01257"></a><span class="lineno"> 1257</span>        <a class="code hl_function" href="namespaceshark.html#a6ae694efca57e84792fcff090223437e" title="Calculates the mean vector of the input vectors.">mean</a> /= (double)<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l01258" name="l01258"></a><span class="lineno"> 1258</span>        RealVector step(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>);</div>
<div class="line"><a id="l01259" name="l01259"></a><span class="lineno"> 1259</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) step(c) = (c == y) ? (mu(c) + <a class="code hl_function" href="namespaceshark.html#a6ae694efca57e84792fcff090223437e" title="Calculates the mean vector of the input vectors.">mean</a>) : (<a class="code hl_function" href="namespaceshark.html#a6ae694efca57e84792fcff090223437e" title="Calculates the mean vector of the input vectors.">mean</a> - mu(c));</div>
<div class="line"><a id="l01260" name="l01260"></a><span class="lineno"> 1260</span>        <a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#a64edc8279169777bf9ef05052a412acd">add_scaled</a>(w, step, <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">m_data</a>[index].input);</div>
<div class="line"><a id="l01261" name="l01261"></a><span class="lineno"> 1261</span>    }</div>
</div>
<div class="line"><a id="l01262" name="l01262"></a><span class="lineno"> 1262</span><span class="comment"></span> </div>
<div class="line"><a id="l01263" name="l01263"></a><span class="lineno"> 1263</span><span class="comment">    /// \brief Solve the sub-problem posed by a single training example.</span></div>
<div class="foldopen" id="foldopen01264" data-start="{" data-end="}">
<div class="line"><a id="l01264" name="l01264"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_a_t_m.html#a2844a08c891b42cacec77f53b4e7a1ce"> 1264</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_a_t_m.html#a2844a08c891b42cacec77f53b4e7a1ce" title="Solve the sub-problem posed by a single training example.">solveSub</a>(<span class="keywordtype">double</span> epsilon, RealVector&amp; gradient, <span class="keywordtype">double</span> q, <span class="keywordtype">double</span> C, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y, blas::dense_vector_adaptor&lt;double&gt;&amp; alpha, RealVector&amp; mu)</div>
<div class="line"><a id="l01265" name="l01265"></a><span class="lineno"> 1265</span>    {</div>
<div class="line"><a id="l01266" name="l01266"></a><span class="lineno"> 1266</span>        <span class="keyword">const</span> <span class="keywordtype">double</span> ood = 1.0 / <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l01267" name="l01267"></a><span class="lineno"> 1267</span>        <span class="keyword">const</span> <span class="keywordtype">double</span> qq = (1.0 - ood) * q;</div>
<div class="line"><a id="l01268" name="l01268"></a><span class="lineno"> 1268</span>        <span class="keywordtype">double</span> gain = 0.0;</div>
<div class="line"><a id="l01269" name="l01269"></a><span class="lineno"> 1269</span> </div>
<div class="line"><a id="l01270" name="l01270"></a><span class="lineno"> 1270</span>        <span class="comment">// SMO loop</span></div>
<div class="line"><a id="l01271" name="l01271"></a><span class="lineno"> 1271</span>        <span class="keywordtype">size_t</span> iter, maxiter = 10 * <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l01272" name="l01272"></a><span class="lineno"> 1272</span>        <span class="keywordflow">for</span> (iter=0; iter&lt;maxiter; iter++)</div>
<div class="line"><a id="l01273" name="l01273"></a><span class="lineno"> 1273</span>        {</div>
<div class="line"><a id="l01274" name="l01274"></a><span class="lineno"> 1274</span>            <span class="comment">// select working set</span></div>
<div class="line"><a id="l01275" name="l01275"></a><span class="lineno"> 1275</span>            std::size_t idx = 0;</div>
<div class="line"><a id="l01276" name="l01276"></a><span class="lineno"> 1276</span>            std::size_t idx_up = 0, idx_down = 0;</div>
<div class="line"><a id="l01277" name="l01277"></a><span class="lineno"> 1277</span>            <span class="keywordtype">bool</span> size2 = <span class="keyword">false</span>;</div>
<div class="line"><a id="l01278" name="l01278"></a><span class="lineno"> 1278</span>            <span class="keywordtype">double</span> kkt = 0.0;</div>
<div class="line"><a id="l01279" name="l01279"></a><span class="lineno"> 1279</span>            <span class="keywordtype">double</span> grad = 0.0;</div>
<div class="line"><a id="l01280" name="l01280"></a><span class="lineno"> 1280</span>            <span class="keywordflow">if</span> (alpha(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>) == C)</div>
<div class="line"><a id="l01281" name="l01281"></a><span class="lineno"> 1281</span>            {</div>
<div class="line"><a id="l01282" name="l01282"></a><span class="lineno"> 1282</span>                <span class="keywordtype">double</span> kkt_up = -1e100, kkt_down = 1e100;</div>
<div class="line"><a id="l01283" name="l01283"></a><span class="lineno"> 1283</span>                <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++)</div>
<div class="line"><a id="l01284" name="l01284"></a><span class="lineno"> 1284</span>                {</div>
<div class="line"><a id="l01285" name="l01285"></a><span class="lineno"> 1285</span>                    <span class="keyword">const</span> <span class="keywordtype">double</span> g = gradient(c);</div>
<div class="line"><a id="l01286" name="l01286"></a><span class="lineno"> 1286</span>                    <span class="keyword">const</span> <span class="keywordtype">double</span> a = alpha(c);</div>
<div class="line"><a id="l01287" name="l01287"></a><span class="lineno"> 1287</span>                    <span class="keywordflow">if</span> (g &gt; kkt_up &amp;&amp; a &lt; C) { kkt_up = g; idx_up = c; }</div>
<div class="line"><a id="l01288" name="l01288"></a><span class="lineno"> 1288</span>                    <span class="keywordflow">if</span> (g &lt; kkt_down &amp;&amp; a &gt; 0.0) { kkt_down = g; idx_down = c; }</div>
<div class="line"><a id="l01289" name="l01289"></a><span class="lineno"> 1289</span>                }</div>
<div class="line"><a id="l01290" name="l01290"></a><span class="lineno"> 1290</span> </div>
<div class="line"><a id="l01291" name="l01291"></a><span class="lineno"> 1291</span>                <span class="keywordflow">if</span> (kkt_up &lt;= 0.0)</div>
<div class="line"><a id="l01292" name="l01292"></a><span class="lineno"> 1292</span>                {</div>
<div class="line"><a id="l01293" name="l01293"></a><span class="lineno"> 1293</span>                    idx = idx_down;</div>
<div class="line"><a id="l01294" name="l01294"></a><span class="lineno"> 1294</span>                    grad = kkt_down;</div>
<div class="line"><a id="l01295" name="l01295"></a><span class="lineno"> 1295</span>                    kkt = -kkt_down;</div>
<div class="line"><a id="l01296" name="l01296"></a><span class="lineno"> 1296</span>                }</div>
<div class="line"><a id="l01297" name="l01297"></a><span class="lineno"> 1297</span>                <span class="keywordflow">else</span></div>
<div class="line"><a id="l01298" name="l01298"></a><span class="lineno"> 1298</span>                {</div>
<div class="line"><a id="l01299" name="l01299"></a><span class="lineno"> 1299</span>                    grad = kkt_up - kkt_down;</div>
<div class="line"><a id="l01300" name="l01300"></a><span class="lineno"> 1300</span>                    kkt = grad;</div>
<div class="line"><a id="l01301" name="l01301"></a><span class="lineno"> 1301</span>                    size2 = <span class="keyword">true</span>;</div>
<div class="line"><a id="l01302" name="l01302"></a><span class="lineno"> 1302</span>                }</div>
<div class="line"><a id="l01303" name="l01303"></a><span class="lineno"> 1303</span>            }</div>
<div class="line"><a id="l01304" name="l01304"></a><span class="lineno"> 1304</span>            <span class="keywordflow">else</span></div>
<div class="line"><a id="l01305" name="l01305"></a><span class="lineno"> 1305</span>            {</div>
<div class="line"><a id="l01306" name="l01306"></a><span class="lineno"> 1306</span>                <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++)</div>
<div class="line"><a id="l01307" name="l01307"></a><span class="lineno"> 1307</span>                {</div>
<div class="line"><a id="l01308" name="l01308"></a><span class="lineno"> 1308</span>                    <span class="keyword">const</span> <span class="keywordtype">double</span> g = gradient(c);</div>
<div class="line"><a id="l01309" name="l01309"></a><span class="lineno"> 1309</span>                    <span class="keyword">const</span> <span class="keywordtype">double</span> a = alpha(c);</div>
<div class="line"><a id="l01310" name="l01310"></a><span class="lineno"> 1310</span>                    <span class="keywordflow">if</span> (g &gt; kkt) { kkt = g; idx = c; }</div>
<div class="line"><a id="l01311" name="l01311"></a><span class="lineno"> 1311</span>                    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (-g &gt; kkt &amp;&amp; a &gt; 0.0) { kkt = -g; idx = c; }</div>
<div class="line"><a id="l01312" name="l01312"></a><span class="lineno"> 1312</span>                }</div>
<div class="line"><a id="l01313" name="l01313"></a><span class="lineno"> 1313</span>                grad = gradient(idx);</div>
<div class="line"><a id="l01314" name="l01314"></a><span class="lineno"> 1314</span>            }</div>
<div class="line"><a id="l01315" name="l01315"></a><span class="lineno"> 1315</span> </div>
<div class="line"><a id="l01316" name="l01316"></a><span class="lineno"> 1316</span>            <span class="comment">// check stopping criterion</span></div>
<div class="line"><a id="l01317" name="l01317"></a><span class="lineno"> 1317</span>            <span class="keywordflow">if</span> (kkt &lt; epsilon) <span class="keywordflow">return</span> gain;</div>
<div class="line"><a id="l01318" name="l01318"></a><span class="lineno"> 1318</span> </div>
<div class="line"><a id="l01319" name="l01319"></a><span class="lineno"> 1319</span>            <span class="keywordflow">if</span> (size2)</div>
<div class="line"><a id="l01320" name="l01320"></a><span class="lineno"> 1320</span>            {</div>
<div class="line"><a id="l01321" name="l01321"></a><span class="lineno"> 1321</span>                <span class="comment">// perform step</span></div>
<div class="line"><a id="l01322" name="l01322"></a><span class="lineno"> 1322</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> a_up = alpha(idx_up);</div>
<div class="line"><a id="l01323" name="l01323"></a><span class="lineno"> 1323</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> a_down = alpha(idx_down);</div>
<div class="line"><a id="l01324" name="l01324"></a><span class="lineno"> 1324</span>                <span class="keywordtype">double</span> m = grad / (2.0 * q);</div>
<div class="line"><a id="l01325" name="l01325"></a><span class="lineno"> 1325</span>                <span class="keywordtype">double</span> a_up_new = a_up + m;</div>
<div class="line"><a id="l01326" name="l01326"></a><span class="lineno"> 1326</span>                <span class="keywordtype">double</span> a_down_new = a_down - m;</div>
<div class="line"><a id="l01327" name="l01327"></a><span class="lineno"> 1327</span>                <span class="keywordflow">if</span> (a_down_new &lt;= 0.0)</div>
<div class="line"><a id="l01328" name="l01328"></a><span class="lineno"> 1328</span>                {</div>
<div class="line"><a id="l01329" name="l01329"></a><span class="lineno"> 1329</span>                    m = a_down;</div>
<div class="line"><a id="l01330" name="l01330"></a><span class="lineno"> 1330</span>                    a_up_new = a_up + m;</div>
<div class="line"><a id="l01331" name="l01331"></a><span class="lineno"> 1331</span>                    a_down_new = 0.0;</div>
<div class="line"><a id="l01332" name="l01332"></a><span class="lineno"> 1332</span>                }</div>
<div class="line"><a id="l01333" name="l01333"></a><span class="lineno"> 1333</span>                alpha(idx_up) = a_up_new;</div>
<div class="line"><a id="l01334" name="l01334"></a><span class="lineno"> 1334</span>                alpha(idx_down) = a_down_new;</div>
<div class="line"><a id="l01335" name="l01335"></a><span class="lineno"> 1335</span>                mu(idx_up) += m;</div>
<div class="line"><a id="l01336" name="l01336"></a><span class="lineno"> 1336</span>                mu(idx_down) -= m;</div>
<div class="line"><a id="l01337" name="l01337"></a><span class="lineno"> 1337</span> </div>
<div class="line"><a id="l01338" name="l01338"></a><span class="lineno"> 1338</span>                <span class="comment">// update gradient and total gain</span></div>
<div class="line"><a id="l01339" name="l01339"></a><span class="lineno"> 1339</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> dg = m * q;</div>
<div class="line"><a id="l01340" name="l01340"></a><span class="lineno"> 1340</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> dgc = dg / <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l01341" name="l01341"></a><span class="lineno"> 1341</span>                <span class="keywordflow">if</span> (idx_up == y)</div>
<div class="line"><a id="l01342" name="l01342"></a><span class="lineno"> 1342</span>                {</div>
<div class="line"><a id="l01343" name="l01343"></a><span class="lineno"> 1343</span>                    <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) gradient(c) -= dgc;</div>
<div class="line"><a id="l01344" name="l01344"></a><span class="lineno"> 1344</span>                    gradient(idx_up) -= dg - 2.0 * dgc;</div>
<div class="line"><a id="l01345" name="l01345"></a><span class="lineno"> 1345</span>                    gradient(idx_down) += dg;</div>
<div class="line"><a id="l01346" name="l01346"></a><span class="lineno"> 1346</span>                }</div>
<div class="line"><a id="l01347" name="l01347"></a><span class="lineno"> 1347</span>                <span class="keywordflow">else</span> <span class="keywordflow">if</span> (idx_down == y)</div>
<div class="line"><a id="l01348" name="l01348"></a><span class="lineno"> 1348</span>                {</div>
<div class="line"><a id="l01349" name="l01349"></a><span class="lineno"> 1349</span>                    gradient(idx_up) -= dg;</div>
<div class="line"><a id="l01350" name="l01350"></a><span class="lineno"> 1350</span>                    gradient(idx_down) += dg - 2.0 * dgc;</div>
<div class="line"><a id="l01351" name="l01351"></a><span class="lineno"> 1351</span>                }</div>
<div class="line"><a id="l01352" name="l01352"></a><span class="lineno"> 1352</span>                <span class="keywordflow">else</span></div>
<div class="line"><a id="l01353" name="l01353"></a><span class="lineno"> 1353</span>                {</div>
<div class="line"><a id="l01354" name="l01354"></a><span class="lineno"> 1354</span>                    gradient(idx_up) -= dg;</div>
<div class="line"><a id="l01355" name="l01355"></a><span class="lineno"> 1355</span>                    gradient(idx_down) += dg;</div>
<div class="line"><a id="l01356" name="l01356"></a><span class="lineno"> 1356</span>                }</div>
<div class="line"><a id="l01357" name="l01357"></a><span class="lineno"> 1357</span>                gain += m * (grad - (dg - dgc));</div>
<div class="line"><a id="l01358" name="l01358"></a><span class="lineno"> 1358</span>            }</div>
<div class="line"><a id="l01359" name="l01359"></a><span class="lineno"> 1359</span>            <span class="keywordflow">else</span></div>
<div class="line"><a id="l01360" name="l01360"></a><span class="lineno"> 1360</span>            {</div>
<div class="line"><a id="l01361" name="l01361"></a><span class="lineno"> 1361</span>                <span class="comment">// perform step</span></div>
<div class="line"><a id="l01362" name="l01362"></a><span class="lineno"> 1362</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> a = alpha(idx);</div>
<div class="line"><a id="l01363" name="l01363"></a><span class="lineno"> 1363</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> a_sum = alpha(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>);</div>
<div class="line"><a id="l01364" name="l01364"></a><span class="lineno"> 1364</span>                <span class="keywordtype">double</span> m = grad / qq;</div>
<div class="line"><a id="l01365" name="l01365"></a><span class="lineno"> 1365</span>                <span class="keywordtype">double</span> a_new = a + m;</div>
<div class="line"><a id="l01366" name="l01366"></a><span class="lineno"> 1366</span>                <span class="keywordtype">double</span> a_sum_new = a_sum + m;</div>
<div class="line"><a id="l01367" name="l01367"></a><span class="lineno"> 1367</span>                <span class="keywordflow">if</span> (a_new &lt;= 0.0)</div>
<div class="line"><a id="l01368" name="l01368"></a><span class="lineno"> 1368</span>                {</div>
<div class="line"><a id="l01369" name="l01369"></a><span class="lineno"> 1369</span>                    m = -a;</div>
<div class="line"><a id="l01370" name="l01370"></a><span class="lineno"> 1370</span>                    a_new = 0.0;</div>
<div class="line"><a id="l01371" name="l01371"></a><span class="lineno"> 1371</span>                    a_sum_new = a_sum + m;</div>
<div class="line"><a id="l01372" name="l01372"></a><span class="lineno"> 1372</span>                }</div>
<div class="line"><a id="l01373" name="l01373"></a><span class="lineno"> 1373</span>                <span class="keywordflow">else</span> <span class="keywordflow">if</span> (a_sum_new &gt;= C)</div>
<div class="line"><a id="l01374" name="l01374"></a><span class="lineno"> 1374</span>                {</div>
<div class="line"><a id="l01375" name="l01375"></a><span class="lineno"> 1375</span>                    m = C - a_sum;</div>
<div class="line"><a id="l01376" name="l01376"></a><span class="lineno"> 1376</span>                    a_sum_new = C;</div>
<div class="line"><a id="l01377" name="l01377"></a><span class="lineno"> 1377</span>                    a_new = a + m;</div>
<div class="line"><a id="l01378" name="l01378"></a><span class="lineno"> 1378</span>                }</div>
<div class="line"><a id="l01379" name="l01379"></a><span class="lineno"> 1379</span>                alpha(idx) = a_new;</div>
<div class="line"><a id="l01380" name="l01380"></a><span class="lineno"> 1380</span>                alpha(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>) = a_sum_new;</div>
<div class="line"><a id="l01381" name="l01381"></a><span class="lineno"> 1381</span>                mu(idx) += m;</div>
<div class="line"><a id="l01382" name="l01382"></a><span class="lineno"> 1382</span> </div>
<div class="line"><a id="l01383" name="l01383"></a><span class="lineno"> 1383</span>                <span class="comment">// update gradient and total gain</span></div>
<div class="line"><a id="l01384" name="l01384"></a><span class="lineno"> 1384</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> dg = m * q;</div>
<div class="line"><a id="l01385" name="l01385"></a><span class="lineno"> 1385</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> dgc = dg / <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l01386" name="l01386"></a><span class="lineno"> 1386</span>                <span class="keywordflow">if</span> (idx == y)</div>
<div class="line"><a id="l01387" name="l01387"></a><span class="lineno"> 1387</span>                {</div>
<div class="line"><a id="l01388" name="l01388"></a><span class="lineno"> 1388</span>                    <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) gradient(c) -= dgc;</div>
<div class="line"><a id="l01389" name="l01389"></a><span class="lineno"> 1389</span>                    gradient(idx) -= dg - 2.0 * dgc;</div>
<div class="line"><a id="l01390" name="l01390"></a><span class="lineno"> 1390</span>                }</div>
<div class="line"><a id="l01391" name="l01391"></a><span class="lineno"> 1391</span>                <span class="keywordflow">else</span></div>
<div class="line"><a id="l01392" name="l01392"></a><span class="lineno"> 1392</span>                {</div>
<div class="line"><a id="l01393" name="l01393"></a><span class="lineno"> 1393</span>                    <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) gradient(c) += (c == y) ? -dgc : dgc;</div>
<div class="line"><a id="l01394" name="l01394"></a><span class="lineno"> 1394</span>                    gradient(idx) -= dg;</div>
<div class="line"><a id="l01395" name="l01395"></a><span class="lineno"> 1395</span>                }</div>
<div class="line"><a id="l01396" name="l01396"></a><span class="lineno"> 1396</span>                gain += m * (grad - 0.5 * (dg - dgc));</div>
<div class="line"><a id="l01397" name="l01397"></a><span class="lineno"> 1397</span>            }</div>
<div class="line"><a id="l01398" name="l01398"></a><span class="lineno"> 1398</span>        }</div>
<div class="line"><a id="l01399" name="l01399"></a><span class="lineno"> 1399</span> </div>
<div class="line"><a id="l01400" name="l01400"></a><span class="lineno"> 1400</span>        <span class="keywordflow">return</span> gain;</div>
<div class="line"><a id="l01401" name="l01401"></a><span class="lineno"> 1401</span>    }</div>
</div>
<div class="line"><a id="l01402" name="l01402"></a><span class="lineno"> 1402</span> </div>
<div class="line"><a id="l01403" name="l01403"></a><span class="lineno"> 1403</span><span class="keyword">protected</span>:</div>
<div class="line"><a id="l01404" name="l01404"></a><span class="lineno"> 1404</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#a64edc8279169777bf9ef05052a412acd">::add_scaled</a>;</div>
<div class="line"><a id="l01405" name="l01405"></a><span class="lineno"> 1405</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">::m_data</a>;</div>
<div class="line"><a id="l01406" name="l01406"></a><span class="lineno"> 1406</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">::m_classes</a>;</div>
<div class="line"><a id="l01407" name="l01407"></a><span class="lineno"> 1407</span>};</div>
</div>
<div class="line"><a id="l01408" name="l01408"></a><span class="lineno"> 1408</span> </div>
<div class="line"><a id="l01409" name="l01409"></a><span class="lineno"> 1409</span><span class="comment"></span> </div>
<div class="line"><a id="l01410" name="l01410"></a><span class="lineno"> 1410</span><span class="comment">/// \brief Solver for the &quot;reinforced&quot; multi-class SVM.</span></div>
<div class="line"><a id="l01411" name="l01411"></a><span class="lineno"> 1411</span><span class="comment"></span><span class="keyword">template</span> &lt;<span class="keyword">class</span> InputT&gt;</div>
<div class="foldopen" id="foldopen01412" data-start="{" data-end="};">
<div class="line"><a id="l01412" name="l01412"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_reinforced.html"> 1412</a></span><span class="keyword">class </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear_reinforced.html" title="Solver for the &quot;reinforced&quot; multi-class SVM.">QpMcLinearReinforced</a> : <span class="keyword">public</span> <a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;</div>
<div class="line"><a id="l01413" name="l01413"></a><span class="lineno"> 1413</span>{</div>
<div class="line"><a id="l01414" name="l01414"></a><span class="lineno"> 1414</span><span class="keyword">public</span>:</div>
<div class="line"><a id="l01415" name="l01415"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_reinforced.html#a6cddfc666a5511751458970c83a0fa82"> 1415</a></span>    <span class="keyword">typedef</span> <a class="code hl_class" href="classshark_1_1_labeled_data.html" title="Data set for supervised learning.">LabeledData&lt;InputT, unsigned int&gt;</a> <a class="code hl_typedef" href="classshark_1_1_qp_mc_linear_reinforced.html#a6cddfc666a5511751458970c83a0fa82">DatasetType</a>;</div>
<div class="line"><a id="l01416" name="l01416"></a><span class="lineno"> 1416</span><span class="comment"></span> </div>
<div class="line"><a id="l01417" name="l01417"></a><span class="lineno"> 1417</span><span class="comment">    /// \brief Constructor</span></div>
<div class="foldopen" id="foldopen01418" data-start="{" data-end="}">
<div class="line"><a id="l01418" name="l01418"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_reinforced.html#a3bd3712996fc586f17118eb739653276"> 1418</a></span><span class="comment"></span>    <a class="code hl_function" href="classshark_1_1_qp_mc_linear_reinforced.html#a3bd3712996fc586f17118eb739653276" title="Constructor.">QpMcLinearReinforced</a>(</div>
<div class="line"><a id="l01419" name="l01419"></a><span class="lineno"> 1419</span>            <span class="keyword">const</span> <a class="code hl_class" href="classshark_1_1_labeled_data.html" title="Data set for supervised learning.">DatasetType</a>&amp; dataset,</div>
<div class="line"><a id="l01420" name="l01420"></a><span class="lineno"> 1420</span>            std::size_t dim,</div>
<div class="line"><a id="l01421" name="l01421"></a><span class="lineno"> 1421</span>            std::size_t classes)</div>
<div class="line"><a id="l01422" name="l01422"></a><span class="lineno"> 1422</span>    : <a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;(dataset, dim, classes)</div>
<div class="line"><a id="l01423" name="l01423"></a><span class="lineno"> 1423</span>    { }</div>
</div>
<div class="line"><a id="l01424" name="l01424"></a><span class="lineno"> 1424</span> </div>
<div class="line"><a id="l01425" name="l01425"></a><span class="lineno"> 1425</span><span class="keyword">protected</span>:<span class="comment"></span></div>
<div class="line"><a id="l01426" name="l01426"></a><span class="lineno"> 1426</span><span class="comment">    /// \brief Compute the gradient from the inner products of the weight vectors with the current sample.</span></div>
<div class="foldopen" id="foldopen01427" data-start="{" data-end="}">
<div class="line"><a id="l01427" name="l01427"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_reinforced.html#ab3ba8e3be351d681e3bbba6da830d6a3"> 1427</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_reinforced.html#ab3ba8e3be351d681e3bbba6da830d6a3" title="Compute the gradient from the inner products of the weight vectors with the current sample.">calcGradient</a>(RealVector&amp; gradient, RealVector wx, blas::dense_vector_adaptor&lt;double const&gt; <span class="keyword">const</span>&amp; alpha, <span class="keywordtype">double</span> C, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y)</div>
<div class="line"><a id="l01428" name="l01428"></a><span class="lineno"> 1428</span>    {</div>
<div class="line"><a id="l01429" name="l01429"></a><span class="lineno"> 1429</span>        <span class="keywordtype">double</span> violation = 0.0;</div>
<div class="line"><a id="l01430" name="l01430"></a><span class="lineno"> 1430</span>        <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++)</div>
<div class="line"><a id="l01431" name="l01431"></a><span class="lineno"> 1431</span>        {</div>
<div class="line"><a id="l01432" name="l01432"></a><span class="lineno"> 1432</span>            <span class="keyword">const</span> <span class="keywordtype">double</span> g = (c == y) ? (<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a> - 1.0) - wx(y) : 1.0 + wx(c);</div>
<div class="line"><a id="l01433" name="l01433"></a><span class="lineno"> 1433</span>            gradient(c) = g;</div>
<div class="line"><a id="l01434" name="l01434"></a><span class="lineno"> 1434</span>            <span class="keywordflow">if</span> (g &gt; violation &amp;&amp; alpha(c) &lt; C) violation = g;</div>
<div class="line"><a id="l01435" name="l01435"></a><span class="lineno"> 1435</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (-g &gt; violation &amp;&amp; alpha(c) &gt; 0.0) violation = -g;</div>
<div class="line"><a id="l01436" name="l01436"></a><span class="lineno"> 1436</span>        }</div>
<div class="line"><a id="l01437" name="l01437"></a><span class="lineno"> 1437</span>        <span class="keywordflow">return</span> violation;</div>
<div class="line"><a id="l01438" name="l01438"></a><span class="lineno"> 1438</span>    }</div>
</div>
<div class="line"><a id="l01439" name="l01439"></a><span class="lineno"> 1439</span><span class="comment"></span> </div>
<div class="line"><a id="l01440" name="l01440"></a><span class="lineno"> 1440</span><span class="comment">    /// \brief Update the weight vectors (primal variables) after a step on the dual variables.</span></div>
<div class="foldopen" id="foldopen01441" data-start="{" data-end="}">
<div class="line"><a id="l01441" name="l01441"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_reinforced.html#a17bbc888e42a6144ab9868f1a821809d"> 1441</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_reinforced.html#a17bbc888e42a6144ab9868f1a821809d" title="Update the weight vectors (primal variables) after a step on the dual variables.">updateWeightVectors</a>(RealMatrix&amp; w, RealVector <span class="keyword">const</span>&amp; mu, std::size_t index)</div>
<div class="line"><a id="l01442" name="l01442"></a><span class="lineno"> 1442</span>    {</div>
<div class="line"><a id="l01443" name="l01443"></a><span class="lineno"> 1443</span>        <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y = <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">m_data</a>[index].label;</div>
<div class="line"><a id="l01444" name="l01444"></a><span class="lineno"> 1444</span>        <span class="keywordtype">double</span> <a class="code hl_function" href="namespaceshark.html#a6ae694efca57e84792fcff090223437e" title="Calculates the mean vector of the input vectors.">mean</a> = -2.0 * mu(y);</div>
<div class="line"><a id="l01445" name="l01445"></a><span class="lineno"> 1445</span>        <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) <a class="code hl_function" href="namespaceshark.html#a6ae694efca57e84792fcff090223437e" title="Calculates the mean vector of the input vectors.">mean</a> += mu(c);</div>
<div class="line"><a id="l01446" name="l01446"></a><span class="lineno"> 1446</span>        <a class="code hl_function" href="namespaceshark.html#a6ae694efca57e84792fcff090223437e" title="Calculates the mean vector of the input vectors.">mean</a> /= (double)<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l01447" name="l01447"></a><span class="lineno"> 1447</span>        RealVector step(<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>);</div>
<div class="line"><a id="l01448" name="l01448"></a><span class="lineno"> 1448</span>        <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) step(c) = ((c == y) ? (mu(c) + <a class="code hl_function" href="namespaceshark.html#a6ae694efca57e84792fcff090223437e" title="Calculates the mean vector of the input vectors.">mean</a>) : (<a class="code hl_function" href="namespaceshark.html#a6ae694efca57e84792fcff090223437e" title="Calculates the mean vector of the input vectors.">mean</a> - mu(c)));</div>
<div class="line"><a id="l01449" name="l01449"></a><span class="lineno"> 1449</span>        <a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#a64edc8279169777bf9ef05052a412acd">add_scaled</a>(w, step, <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">m_data</a>[index].input);</div>
<div class="line"><a id="l01450" name="l01450"></a><span class="lineno"> 1450</span>    }</div>
</div>
<div class="line"><a id="l01451" name="l01451"></a><span class="lineno"> 1451</span><span class="comment"></span> </div>
<div class="line"><a id="l01452" name="l01452"></a><span class="lineno"> 1452</span><span class="comment">    /// \brief Solve the sub-problem posed by a single training example.</span></div>
<div class="foldopen" id="foldopen01453" data-start="{" data-end="}">
<div class="line"><a id="l01453" name="l01453"></a><span class="lineno"><a class="line" href="classshark_1_1_qp_mc_linear_reinforced.html#aa5609174ae0b3735e073e828f2a8839b"> 1453</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_qp_mc_linear_reinforced.html#aa5609174ae0b3735e073e828f2a8839b" title="Solve the sub-problem posed by a single training example.">solveSub</a>(<span class="keywordtype">double</span> epsilon, RealVector&amp; gradient, <span class="keywordtype">double</span> q, <span class="keywordtype">double</span> C, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> y, blas::dense_vector_adaptor&lt;double&gt;&amp; alpha, RealVector&amp; mu)</div>
<div class="line"><a id="l01454" name="l01454"></a><span class="lineno"> 1454</span>    {</div>
<div class="line"><a id="l01455" name="l01455"></a><span class="lineno"> 1455</span>        <span class="keyword">const</span> <span class="keywordtype">double</span> ood = 1.0 / <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l01456" name="l01456"></a><span class="lineno"> 1456</span>        <span class="keyword">const</span> <span class="keywordtype">double</span> qq = (1.0 - ood) * q;</div>
<div class="line"><a id="l01457" name="l01457"></a><span class="lineno"> 1457</span>        <span class="keywordtype">double</span> gain = 0.0;</div>
<div class="line"><a id="l01458" name="l01458"></a><span class="lineno"> 1458</span> </div>
<div class="line"><a id="l01459" name="l01459"></a><span class="lineno"> 1459</span>        <span class="comment">// SMO loop</span></div>
<div class="line"><a id="l01460" name="l01460"></a><span class="lineno"> 1460</span>        <span class="keywordtype">size_t</span> iter, maxiter = 10 * <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l01461" name="l01461"></a><span class="lineno"> 1461</span>        <span class="keywordflow">for</span> (iter=0; iter&lt;maxiter; iter++)</div>
<div class="line"><a id="l01462" name="l01462"></a><span class="lineno"> 1462</span>        {</div>
<div class="line"><a id="l01463" name="l01463"></a><span class="lineno"> 1463</span>            <span class="comment">// select working set</span></div>
<div class="line"><a id="l01464" name="l01464"></a><span class="lineno"> 1464</span>            std::size_t idx = 0;</div>
<div class="line"><a id="l01465" name="l01465"></a><span class="lineno"> 1465</span>            <span class="keywordtype">double</span> kkt = 0.0;</div>
<div class="line"><a id="l01466" name="l01466"></a><span class="lineno"> 1466</span>            <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++)</div>
<div class="line"><a id="l01467" name="l01467"></a><span class="lineno"> 1467</span>            {</div>
<div class="line"><a id="l01468" name="l01468"></a><span class="lineno"> 1468</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> g = gradient(c);</div>
<div class="line"><a id="l01469" name="l01469"></a><span class="lineno"> 1469</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> a = alpha(c);</div>
<div class="line"><a id="l01470" name="l01470"></a><span class="lineno"> 1470</span>                <span class="keywordflow">if</span> (g &gt; kkt &amp;&amp; a &lt; C) { kkt = g; idx = c; }</div>
<div class="line"><a id="l01471" name="l01471"></a><span class="lineno"> 1471</span>                <span class="keywordflow">else</span> <span class="keywordflow">if</span> (-g &gt; kkt &amp;&amp; a &gt; 0.0) { kkt = -g; idx = c; }</div>
<div class="line"><a id="l01472" name="l01472"></a><span class="lineno"> 1472</span>            }</div>
<div class="line"><a id="l01473" name="l01473"></a><span class="lineno"> 1473</span> </div>
<div class="line"><a id="l01474" name="l01474"></a><span class="lineno"> 1474</span>            <span class="comment">// check stopping criterion</span></div>
<div class="line"><a id="l01475" name="l01475"></a><span class="lineno"> 1475</span>            <span class="keywordflow">if</span> (kkt &lt; epsilon) <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l01476" name="l01476"></a><span class="lineno"> 1476</span> </div>
<div class="line"><a id="l01477" name="l01477"></a><span class="lineno"> 1477</span>            <span class="comment">// perform step</span></div>
<div class="line"><a id="l01478" name="l01478"></a><span class="lineno"> 1478</span>            <span class="keyword">const</span> <span class="keywordtype">double</span> a = alpha(idx);</div>
<div class="line"><a id="l01479" name="l01479"></a><span class="lineno"> 1479</span>            <span class="keyword">const</span> <span class="keywordtype">double</span> g = gradient(idx);</div>
<div class="line"><a id="l01480" name="l01480"></a><span class="lineno"> 1480</span>            <span class="keywordtype">double</span> m = g / qq;</div>
<div class="line"><a id="l01481" name="l01481"></a><span class="lineno"> 1481</span>            <span class="keywordtype">double</span> a_new = a + m;</div>
<div class="line"><a id="l01482" name="l01482"></a><span class="lineno"> 1482</span>            <span class="keywordflow">if</span> (a_new &lt;= 0.0)</div>
<div class="line"><a id="l01483" name="l01483"></a><span class="lineno"> 1483</span>            {</div>
<div class="line"><a id="l01484" name="l01484"></a><span class="lineno"> 1484</span>                m = -a;</div>
<div class="line"><a id="l01485" name="l01485"></a><span class="lineno"> 1485</span>                a_new = 0.0;</div>
<div class="line"><a id="l01486" name="l01486"></a><span class="lineno"> 1486</span>            }</div>
<div class="line"><a id="l01487" name="l01487"></a><span class="lineno"> 1487</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (a_new &gt;= C)</div>
<div class="line"><a id="l01488" name="l01488"></a><span class="lineno"> 1488</span>            {</div>
<div class="line"><a id="l01489" name="l01489"></a><span class="lineno"> 1489</span>                m = C - a;</div>
<div class="line"><a id="l01490" name="l01490"></a><span class="lineno"> 1490</span>                a_new = C;</div>
<div class="line"><a id="l01491" name="l01491"></a><span class="lineno"> 1491</span>            }</div>
<div class="line"><a id="l01492" name="l01492"></a><span class="lineno"> 1492</span>            alpha(idx) = a_new;</div>
<div class="line"><a id="l01493" name="l01493"></a><span class="lineno"> 1493</span>            mu(idx) += m;</div>
<div class="line"><a id="l01494" name="l01494"></a><span class="lineno"> 1494</span> </div>
<div class="line"><a id="l01495" name="l01495"></a><span class="lineno"> 1495</span>            <span class="comment">// update gradient and total gain</span></div>
<div class="line"><a id="l01496" name="l01496"></a><span class="lineno"> 1496</span>            <span class="keyword">const</span> <span class="keywordtype">double</span> dg = m * q;</div>
<div class="line"><a id="l01497" name="l01497"></a><span class="lineno"> 1497</span>            <span class="keyword">const</span> <span class="keywordtype">double</span> dgc = dg / <a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>;</div>
<div class="line"><a id="l01498" name="l01498"></a><span class="lineno"> 1498</span>            <span class="keywordflow">if</span> (idx == y)</div>
<div class="line"><a id="l01499" name="l01499"></a><span class="lineno"> 1499</span>            {</div>
<div class="line"><a id="l01500" name="l01500"></a><span class="lineno"> 1500</span>                <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) gradient(c) -= dgc;</div>
<div class="line"><a id="l01501" name="l01501"></a><span class="lineno"> 1501</span>                gradient(idx) -= dg - 2.0 * dgc;</div>
<div class="line"><a id="l01502" name="l01502"></a><span class="lineno"> 1502</span>            }</div>
<div class="line"><a id="l01503" name="l01503"></a><span class="lineno"> 1503</span>            <span class="keywordflow">else</span></div>
<div class="line"><a id="l01504" name="l01504"></a><span class="lineno"> 1504</span>            {</div>
<div class="line"><a id="l01505" name="l01505"></a><span class="lineno"> 1505</span>                <span class="keywordflow">for</span> (std::size_t c=0; c&lt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">m_classes</a>; c++) gradient(c) += (c == y) ? -dgc : dgc;</div>
<div class="line"><a id="l01506" name="l01506"></a><span class="lineno"> 1506</span>                gradient(idx) -= dg;</div>
<div class="line"><a id="l01507" name="l01507"></a><span class="lineno"> 1507</span>            }</div>
<div class="line"><a id="l01508" name="l01508"></a><span class="lineno"> 1508</span> </div>
<div class="line"><a id="l01509" name="l01509"></a><span class="lineno"> 1509</span>            gain += m * (g - 0.5 * (dg - dgc));</div>
<div class="line"><a id="l01510" name="l01510"></a><span class="lineno"> 1510</span>        }</div>
<div class="line"><a id="l01511" name="l01511"></a><span class="lineno"> 1511</span> </div>
<div class="line"><a id="l01512" name="l01512"></a><span class="lineno"> 1512</span>        <span class="keywordflow">return</span> gain;</div>
<div class="line"><a id="l01513" name="l01513"></a><span class="lineno"> 1513</span>    }</div>
</div>
<div class="line"><a id="l01514" name="l01514"></a><span class="lineno"> 1514</span> </div>
<div class="line"><a id="l01515" name="l01515"></a><span class="lineno"> 1515</span><span class="keyword">protected</span>:</div>
<div class="line"><a id="l01516" name="l01516"></a><span class="lineno"> 1516</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_function" href="classshark_1_1_qp_mc_linear.html#a64edc8279169777bf9ef05052a412acd">::add_scaled</a>;</div>
<div class="line"><a id="l01517" name="l01517"></a><span class="lineno"> 1517</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#ab724fc27e23748209c439970919afdc1" title="view on training data">::m_data</a>;</div>
<div class="line"><a id="l01518" name="l01518"></a><span class="lineno"> 1518</span>    <span class="keyword">using </span><a class="code hl_class" href="classshark_1_1_qp_mc_linear.html" title="Generic solver skeleton for linear multi-class SVM problems.">QpMcLinear</a>&lt;InputT&gt;<a class="code hl_variable" href="classshark_1_1_qp_mc_linear.html#a3deaa3c8d8f3b5a15ffc509ed17a0398" title="number of classes">::m_classes</a>;</div>
<div class="line"><a id="l01519" name="l01519"></a><span class="lineno"> 1519</span>};</div>
</div>
<div class="line"><a id="l01520" name="l01520"></a><span class="lineno"> 1520</span> </div>
<div class="line"><a id="l01521" name="l01521"></a><span class="lineno"> 1521</span> </div>
<div class="line"><a id="l01522" name="l01522"></a><span class="lineno"> 1522</span>}</div>
<div class="line"><a id="l01523" name="l01523"></a><span class="lineno"> 1523</span><span class="preprocessor">#endif</span></div>
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